The New Sudoku Players' Forum

by **rjamil** » Sat Feb 04, 2017 7:54 pm

Hi all,

I am sharing herewith strategy discussed here, i.e., Irregular XYZ-Wings strategy.

As per my understanding, Irregular XYZ-Wings strategy is summarized as follows:

Code: Select all: ----------+----------+---------- . xyz . | . . yz | +z +z +z . . . | . . . | / / / . . xz | -z -z -z | +z +z +z ----------+----------+----------

1) Irregular XYZ-Wings strategy is based on three cells, i.e., one pivot cell and two pincer cells that contain exactly three values and align within a chute;
2) Pivot cell contains all three values and pincer cells contain two values each;
3) First pincer cell align with pivot cell's line;
4) Second pincer cell contains only one common value with first pincer cell and align with pivot cell's box but not first pincer cell's line;
5) Box that do not contain pivot cell and pincer cells; and contain pincer cells common value anywhere within both pivot cell and pincer cells lines only;
6) Pincer cell's common value may me eliminated from cells align with first pincer cell's box and second pincer cell's line.

However, Irregular WXYZ-Wings strategy, also mentioned in original site discussion, is under further studying phase.

R. Jamil

by **rjamil** » Sun Feb 05, 2017 2:49 am

Hi again,

I have studied all combinations of Irregular WXYZ-Wings as follows:

Code: Select all: --------------+-------------+----------- 01) . wz . | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . xz yz | +z +z +z --------------+-------------+----------- 02) . xz yz | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . wz . | +z +z +z --------------+-------------+----------- 03) . wz . | +z +z +z | -z -z -z . . . | / / / | . . . . wxyz . | +z xz +z | . yz . --------------+-------------+----------- 04) . wz . | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . xz . | +z yz +z --------------+-------------+----------- 05) . wz . | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . xy yz | +z +z +z --------------+-------------+----------- 06) . xy yz | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . wz . | +z +z +z --------------+-------------+----------- 07) . wz . | +z +z +z | -z -z -z . . . | / / / | . . . . wxyz . | +z xy +z | . yz . --------------+-------------+----------- 08) . wz . | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . xy xyz | +z +z +z --------------+-------------+----------- 09) . xy xyz | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . wz . | +z +z +z --------------+-------------+----------- 10) . wz . | +z +z +z | -z -z -z . . . | / / / | . . . . wxyz . | +z xy +z | . xyz . --------------+-------------+----------- 11) . wz . | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . xz xyz | +z +z +z --------------+-------------+----------- 12) . xz xyz | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . wz . | +z +z +z --------------+-------------+----------- 13) . wz . | +z +z +z | -z -z -z . . . | / / / | . . . . wxyz . | +z xz +z | . xyz . --------------+-------------+----------- 14) . wz . | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . xz . | +z xyz +z --------------+-------------+----------- 15) . wz . | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . xyz xyz | +z +z +z --------------+-------------+----------- 16) . xyz xyz | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . wz . | +z +z +z --------------+-------------+----------- 17) . wz . | +z +z +z | -z -z -z . . . | / / / | . . . . wxyz . | +z xyz +z | . xyz . --------------+-------------+----------- 18) . wz . | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . xyz . | +z xyz +z --------------+-------------+-----------

1) Irregular WXYZ-Wing strategy is based on four cells within a chute, i.e., one pivot cell and three pincer cells that contain exactly four values and align within a chute;
2) Pivot cell contains all four values;
3) First pincer cell align with pivot cell's line;
4) Second pincer cell align with pivot cell's box but not first pincer cell's line;
5) Third pincer cell align with either a) pivot cell's line and first pincer cell's box; first and third pincer cell contain three values and second pincer cell contain two values; or b) pivot cell's box and second pincer cell's line; second and third pincer cells contain three values and first pincer cell contain two values;
6) Pincer cells contain only one common value;
7) Box that do not contain second and/or third pincer cell(s) and only contain pincer cells common value within pivot and pincer cells line;
8) Pincer cell's common value may me eliminated from cells align with either first or third pincer cell's box and second pincer cell's line.

R. Jamil

20170210: Typos:-
#18 exemplar corrected as per StrmCkr pointed out below.
20170211: Typos:-
In WXYZ-Wings, point 7 should start as "Box that do not contain ..."

by **rjamil** » Thu Feb 09, 2017 9:05 am

Hi all,

I am studying new strategies one by one. Specially interested in pattern strategy at the moment and looking for variations of already programmed strategies.

Having come to know XY-Wings and XYZ-Wings Transport strategy, which also seems to me look like Irregular XYZ-Wings strategy (which is currently under study phase) and/or XYZ-Wings Hybrid strategy (already programmed).

Is Wings Transport strategy either completely overlap or similar or identical to Irregular Wings strategy and/or Wings Hybrid strategy or vice versa?

Will someone please give exemplar form of Wings Transport and Irregular Wings strategies (if different) along with all variations of them to easy understanding.

I am sharing herewith the XYZ-Wings Hybrid exemplars below:

Code: Select all: Type 1:- -----------+----------+---------- . xyz . | . . yz | -Z -Z -Z . . . | . . . | . . . . . xz | . yz . | . . . -----------+----------+---------- Type 2:- -----------+----------+---------- . xyz . | . . yz | . . . -Z -Z -Z | . . . | . . . . . xz | . xz . | . . . -----------+----------+----------

R. Jamil

by **StrmCkr** » Fri Feb 10, 2017 1:51 am

The irregular wing strategy is alot more complex then your simplified examples, it takes any singular digit and expands it to any lenght across the entire grid as long as the end point of the chain connects visually or completely back onto some kind of technique not just limited to xy, xyz, Wxyz,
vwxyz, uvwxyz, tuvwxyz, stuvwxyz, (note : any of the bent "wing" above size 4 isn't documented and are used infrequently )
W-wings
M-wings
L-wing,
S-wings
Hybrid wings. {pattern defined but no developed thread with examples as it has way to many to display them all. }

Most would contain the digit length to short chains as a manual solver.

I do have a thread that shows cases a tip of an ice Burg on its potential as I use uncompleted fish patterns bridged to any technique to complete the fish. {which is the same thing that's going on here you have a incomplete 1 fish for a box being completed by mapping it to a wxyz-wing}

(it's possible to do incomplete and completed patterns in unison)

Finned transport is the same concept as irregular wings from what I understand from reading daily sudoku forums.

Usually the chain length is kept short, and the connecting patterns are basic and easy to follow.

Ps. #18 example has an error the-z in the last box should be +z

Code: Select all: 18) . wz . | -z -z -z | +z +z +z . . . | . . . | / / / . wxyz . | . xyz . | +z xyz +z

by **rjamil** » Fri Feb 10, 2017 8:01 pm

Hi StrmCkr,

I read your link and what I understand for irregular wings strategy at either useless or flightless or spent wings strategy is as follows:

Code: Select all: Irregular XY-Wings Row-Column or Column-Row wise:- -----------+-----------+---------- 1) . . . | / +z / | . . . . xy . | +z +z +z | . x-Z . . . . | / +z / | . . . -----------+-----------+---------- . . . | . . . | . . . / yz / | / +z / | / / / . . . | . . . | . . . -----------+-----------+---------- Irregular XY-Wings Box-Line wise:- -----------+-----------+---------- 1) . xy . | / / yz | . . . . . . | / / / | . . . . . x-Z | +z +z / | . . . -----------+-----------+---------- 2) . xy . | . . y-Z | . . . . . . | . . . | . . . / / xz | +z +z / | / / / -----------+-----------+---------- Irregular XYZ-Wings Box-Line wise:- -----------+-----------+---------- 1) . xyz . | . . yz | +z +z +z . . . | . . . | / / / . . xz | -Z -Z / | +z +z +z -----------+-----------+----------

Also, two missing Irregular WXYZ-Wings from my second post of this thread are as follows:

Code: Select all: Irregular WXYZ-Wings Box-Line wise;- --------------+-------------+----------- aa) . xy . | . . . | / / / . . yz | -Z -Z -Z | +z +z +z . wxyz . | . wz . | +z +z +z --------------+-------------+----------- bb) . xy . | . . . | / / / . xyz | -Z -Z -Z | +z +z +z . wxyz . | . wz . | +z +z +z --------------+-------------+-----------

Hope that, after including the above exemplars, will complete the Irregular wings patterns.

Still not clear about wings transport strategy.

Also, still not clear about whether wings hybrid strategy fully discovered or not.

Also, not clear about separate naming of transport, hybrid and irregular wings or all same.

R. Jamil

by **StrmCkr** » Sat Feb 11, 2017 7:16 am

Code: Select all: Irregular XY-Wings Row-Column or Column-Row wise:- -----------+-----------+---------- 1) . . . | / +z / | . . . . xy . | +z +z +z | . x-Z . . . . | / +z / | . . . -----------+-----------+---------- . . . | . . . | . . . / yz / | / +z / | / / / . . . | . . . | . . . -----------+-----------+---------- Irregular XY-Wings Box-Line wise:- -----------+-----------+---------- 1) . xy . | / / yz | . . . . . . | / / / | . . . . . x-Z | +z +z / | . . . -----------+-----------+---------- 2) . xy . | . . y-Z | . . . . . . | . . . | . . . / / xz | +z +z / | / / / -----------+-----------+----------

some technical errors in these 3 the patterns its self cannot delete the -z as noted.

{ the error is visible when setting specific cells to 'z' then the pattern cannot see or force a contradiction on the cell placed thus they are invalid elimination!}

my thread uses "Strong" links between marked cells A & B, linked to a fish.

wings are a collection of cells with a relation ship between where said digits can be placed within the set of cells. not quite the same as a strong -weak link relation ship between singular digits.

however the concept is the same take a "pattern" {spent/ useless etc} of some sort and extend it with a fish. {spent/ useless etc} to perhaps make an extra elimination.

ps. the strong link between z's on the row are not needed for this to function in the ERI pattern
you can just use the box!

the following do work.

Code: Select all: Irregular XY-Wings Row-Column or Column-Row wise:- + box ERI -----------+-----------+---------- ) . . . | / +z / | . . . . xy . | +z +z +z | . xZ . . . . | / +z / | . . . -----------+-----------+---------- . . . | . . . | . . . . yz . | . -z . | . -z . . . . | . . . | . . . -----------+-----------+----------

Code: Select all: Irregular XY-Wings Row-Column or Column-Row wise:- + box ERI -----------+-----------+---------- ) . . . | . . . | . . . . xy . | . -z . | . xZ . . . . | . . . | . . . -----------+-----------+---------- . . . | / z / | . . . . yz . | z z z | . -z . . . . | / z / | . . . -----------+-----------+----------

Code: Select all: -----------+-----------+---------- ) . . . | . . . | . . . . xy . | . . . | . xZ . / / / | / z / | z z z -----------+-----------+---------- . . . | . . . | . . . . yz . | . -z . | . -z . . . . | . . . | . . . -----------+-----------+----------

Code: Select all: -----------+-----------+---------- ) . -z . | . . . | . . . . xy . | . . . | . xZ . / / z | / / / | z z z -----------+-----------+---------- . . -z | . . . | . . . . yz -z | . . . | . -z . . . -z | . . . | . . . -----------+-----------+----------

Code: Select all: -----------+-----------+---------- ) . . / | . . . | . . . . xy / | . . . | . xZ . . . / | . . . | . . . -----------+-----------+---------- . . z | . . . | . . . . yz z | . . . | . -z . . . z | . . . | . . . -----------+-----------+---------- . . / | . . . | . . . . . z | . . . | . -z . . . / | . . . | . . .

Code: Select all: -----------+-----------+---------- ) . . / | . . . | . . . -z xy / | . . . | . xZ . . . z | . . . | -z -z -z -----------+-----------+---------- . . z | . . . | . . . . yz z | . . . | . -z . . . z | . . . | . . . -----------+-----------+---------- . . / | . . . | . . . . . / | . . . | . . . . . / | . . . | . . .

Code: Select all: Irregular XY-Wings Row+ col with link on Columns. -----------+-----------+---------- ) . . . | . / . | . . . -z xy -z | -z z -z | -z xZ -z . . . | . / . | . . . -----------+-----------+---------- . . . | . / . | . . . -z yz -z | -z z -z | -z -z -z . . . | . / . | . . . -----------+-----------+---------- . . . | . / . | . . . . . . | . / . | . . . . . . | . / . | . . . -----------+-----------+----------

Code: Select all: ----------+-----------+---------- ) -z xy -z | z z yz | -z -z -z . . . | / / / | . . . . . xZ | z z z | . . . -----------+-----------+----------

Code: Select all: -----------+-----------+---------- 2) -z xy -z | -z -z yZ | z z z . . . | . . . | / / / -z -z xz | -z -z -z | z z z -----------+-----------+----------

to answer your questiond:
Transport and irregular "wings" are identical concepts
as they both are linking fish cycles to a pattern. {ie the strong weak relation ship between digits and the sector used}

hybrid use specific cells and do not use the strong/weak relation ship in the sector for specific digits.

by **rjamil** » Fri Feb 17, 2017 4:34 pm

***** Re-updated as on 20181202 *****
[hide]20180521 Added: C) XYZ-Wing Transport Box-Line wise, exemplars 3 & 4.
20180606 Added: A) exemplars 21 to 24.
20180608 Added: A) exemplars 29 37 to 32 40; and 37 45 to 40 48.
20180925 Added: B) exemplars 09-16, 19-20, 23.
20181005 Added: A) missing exemplars 55-56.
20181031 Reordered: B) XY-Wing Type 2 Transport Box-Line wise;
Updated: B) In exemplars 17 & 21, -Z @ r5c5;
In exemplars 19 & 23, -Z @ r5c3;
Refreshed: C) XYZ-Wing Transport Box-line wise.
20181111 Added: A) missing exemplars 41-44, 49-52.
20181202 Added: A) additional exclusions in following exemplars:
1) In XY-Wing Type 1 (Row-Column wise) Transport: A) Exemplars 55 & 56
2) In XY-Wing Type 2 (Box-Line wise) Transport: B) Exemplar 15
3) In XYZ-Wing Transport (Box-Line wise): C) Exemplar 11
4) In XYZ-Transport (Row-Column wise): Exemplars 55 & 56
B) additional exemplars in following moves:
1) XY-Wing (Box-Line wise) Transport: B) exemplars 24 & 25
2) XYZ-Wing (Box-Line wise) Transport: C) exemplars 23 & 24
C) Added XYZ-Transport as point "H": here[/hide]

Hi StrmCkr,

First of all, many thanks to StrmCkr for detailed and such multiple helpful and informative guidance either by posts or other threads or through pm.

However, I am still digesting Wings Transport move's patterns slowly.

Here I am sharing StrmCkr's provided exemplars again with labeling and some minor changes as what I understand up till now:

A) XY-Wing Type 1 Transport (Row-Column wise):-

Hidden Text: Show

Code: Select all: ERI --------------+-------------+----------- --------------+-------------+----------- 01) . . . | / +z / | . . . 02) . . . | . . . | . . . . xy . | +z +z +z | . xz . . xy . | . . . | . xz . . . . | / +z / | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . / +z / | . . . | . . . . . . | . . . | . . . +z +z +z | . . . | . -Z . . . . | . . . | . . . / +z / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . -Z . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 03) . . . | . . . | . . . 04) . . . | . . . | . . . . xy . | . -Z . | . xz . . xy . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | / +z / . . . | . . . | . . . . -Z . | . . . | +z +z +z . . . | . . . | . . . . . . | . . . | / +z / --------------+-------------+----------- --------------+-------------+----------- . . . | / +z / | . . . . . . | . . . | . . . . yz . | +z +z +z | . -z . . yz . | . . . | . -z . . . . | / +z / | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Reduced ERI --------------+-------------+----------- --------------+-------------+----------- 05) . -Z . | / +Z / | . . . 06) . . . | . . . | . . . . xy . | +z +z +z | . xz . -Z xy . | . . . | . xz . . . . | / / / | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . / +z / | . . . | . . . . . . | . . . | . . . +Z +z / | . . . | . -Z . . . . | . . . | . . . / +z / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . -Z . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 07) . . . | . . . | . . . 08) . . . | . . . | . . . . xy . | . -Z . | . xz . . xy . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | / +z / . . . | . . . | . . . . -Z . | . . . | / +z +Z . . . | . . . | . . . . . . | . . . | / +z / --------------+-------------+----------- --------------+-------------+----------- . . . | / / / | . . . . . . | . . . | . . . . yz . | +z +z +z | . -z . . yz . | . . . | . -z -Z . . . | / +Z / | . -Z . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Box --------------+-------------+----------- --------------+-------------+----------- 09) . -Z . | +z +z +z | . . . 10) . . . | . . . | . . . . xy . | +z +z +z | . xz . -Z xy . | . . . | . xz . . . . | / / / | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . . . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 11) . . . | . . . | . . . 12) . . . | . . . | . . . . xy . | . . . | . xz . . xy . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | / +z +z . . . | . . . | . . . . . . | . . . | / +z +z . . . | . . . | . . . . . . | . . . | / +z +z --------------+-------------+----------- --------------+-------------+----------- . . . | / / / | . . . . . . | . . . | . . . . yz . | +z +z +z | . -z . . yz . | . . . | . -z -Z . . . | +z +z +z | . -Z . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line --------------+-------------+----------- --------------+-------------+----------- 13) . -Z . | . . . | . . . 14) . . +z | . . . | . . . . xy . | . . . | . xz . -Z xy +z | . . . | . xz . +z +z +z | / / / | +z +z +z . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . +z | . . . | . . . . yz . | . . . | . -z . . yz +z | . . . | . -z . . . . | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 15) . . . | . . . | . . . 16) . . . | . . . | +z . . . xy . | . . . | . xz . . xy . | . . . | +z xz . . . . | . . . | . . . . . . | . . . | +z . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . --------------+-------------+----------- --------------+-------------+----------- +z +z +z | / / / | +z +z +z . . . | . . . | +z . . . yz . | . . . | . -z . . yz . | . . . | +z -z -Z . . . | . . . | . -Z . . . . | . . . | +z . . --------------+-------------+----------- --------------+-------------+----------- Line Reduced Ring --------------+-------------+----------- --------------+-------------+----------- 17) . -YZ . | . . . | -Z . -Z 18) . -Y / | . . . | . . . -X xy -X | -X -X -X |-XZ xz -XZ -XZ xy +Z-X | -XZ -XZ -XZ |-XZ xz -XZ / +Z-Y / | / / / | +z +z +z . -Y / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . -YZ . | . . . | . . . . -Y / | . . . | . . . . -YZ . | . . . | . . . . -Y / | . . . | . . . . -YZ . | . . . | . . . . -Y / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . -YZ . | . . . | . . . -Z -YZ +z | . . . | . . . . yz . | . . . | . -z . . yz +z | . . . | . -z . . -YZ . | . . . | . . . -Z -YZ +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 19) . -Y . | . . . | . -Z . 20) . -Y . | . . . | +z -Z -Z -X xy -X | -X -X -X | -X xz -X -X xy -X | -X -X -X |+z-X xz -X . -Y . | . . . | . -Z . . -Y . | . . . | +z -Z -Z --------------+-------------+----------- --------------+-------------+----------- . -Y . | . . . | . -Z . . -Y . | . . . | / . . . -Y . | . . . | . -Z . . -Y . | . . . | / . . . -Y . | . . . | . -Z . . -Y . | . . . | / . . --------------+-------------+----------- --------------+-------------+----------- +z +z-Y +z | / / / | / +Z / . -Y . | . . . | / . . -Z yz -Z | . . . | . -z . -Z yz -Z | -Z -Z -Z | +Z -z -Z -Z -Y -Z | . . . | . -Z . . -Y . | . . . | / . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 21) . -YZ . | . . . | -Z -Z -Z 22) . -Y / | . . . | . . . -X xy -X | -X -X -X | -XZ xz -XZ -XZ xy +Z-X | -XZ -XZ -XZ | -XZ xz -XZ / +Z-Y / | / / / | / +Z / . -Y / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . -YZ . | . . . | . -Z . . -Y / | . . . | . . . . -YZ . | . . . | . -Z . . -Y / | . . . | . . . . -YZ . | . . . | . -Z . . -Y / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . -YZ . | . . . | . -Z . -Z -YZ / | . . . | . . . . yz . | . . . | . -z . -Z yz +Z | -Z -Z -Z | -Z -z -Z . -YZ . | . . . | . -Z . -Z -YZ / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 23) . -YZ . | . . . | . -Z . 24) . -Y . | . . . | / -Z -Z -X xy -X | -X -X -X | -X xz -X -XZ xy -XZ | -XZ -XZ -XZ |+Z-X xz -XZ . -YZ . | . . . | . -Z . . -Y . | . . . | / -Z -Z --------------+-------------+----------- --------------+-------------+----------- . -YZ . | . . . | . -Z . . -Y . | . . . | / . . . -YZ . | . . . | . -Z . . -Y . | . . . | / . . . -YZ . | . . . | . -Z . . -Y . | . . . | / . . --------------+-------------+----------- --------------+-------------+----------- / +Z-Y / | / / / | / +Z / . -Y . | . . . | / . . -Z yz -Z | . . . | . -z . -Z yz -Z | -Z -Z -Z | +Z -z -Z -Z -YZ -Z | . . . | . -Z . . -Y . | . . . | / . . --------------+-------------+----------- --------------+-------------+----------- Line --------------+-------------+----------- --------------+-------------+----------- 25) . -Z . | . . . | . . . 26) . . / | . . . | . . . . xy . | . . . | . xz . -Z xy / | . . . | . xz . / / +Z | / / / | +z +z +z . . +Z | . . . | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . +z | . . . | . . . . yz -Z | . . . | . -z . . yz +z | . . . | . -z . . . -Z | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 27) . . . | . . . | -Z . . 28) . . . | . . . | +z . . . xy . | . . . | -Z xz . . xy . | . . . | +z xz . . . . | . . . | -Z . . . . . | . . . | +z . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . --------------+-------------+----------- --------------+-------------+----------- +z +z +z | / / / | +Z / / -Z -Z -Z | . . . | +Z . . . yz . | . . . | . -z . . yz . | . . . | / -z -Z . . . | . . . | . -Z . . . . | . . . | / . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 29) . . . | . . . | . . . 30) . . / | . . . | . . . . xy . | . . . | . xz . . xy / | . . . | . xz . / / / | / +Z / | +z +z +z . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . +Z | . . . | . -Z . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . +z | . . . | . . . . yz . | . -Z . | . -z . . yz +z | . . . | . -z . . . . | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 31) . . . | . . . | . . . 32) . . . | . . . | +z . . . xy . | . -Z . | . xz . . xy . | . . . | +z xz . . . . | . . . | . . . . . . | . . . | +z . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . -Z . | . . . | +Z . . . . . | . . . | . . . . . . | . . . | / . . --------------+-------------+----------- --------------+-------------+----------- +z +z +z | / +Z / | / / / . . . | . . . | / . . . yz . | . . . | . -z . . yz . | . . . | / -z . . . . | . . . | . . . . . . | . . . | / . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 33) . . . | . . . | . . . 34) . . / | . . . | . . . . xy . | -Z -Z -Z | . xz . . xy +Z | . . . | . xz . / +Z / | +z +z +z | / / / . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . -Z +z | . . . | . . . . . . | . . . | . . . . -Z +z | . . . | . . . . . . | . . . | . . . . -Z +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . yz . | . . . | . -z . . yz / | . . . | . -z . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 35) . . . | . . . | . . . 36) . . . | . . . | / . . . xy . | . . . | . xz . . xy . | . . . | / xz . . . . | . . . | . . . . . . | . . . | / . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | +z -Z . . . . | . . . | . . . . . . | . . . | +z -Z . . . . | . . . | . . . . . . | . . . | +z -Z . --------------+-------------+----------- --------------+-------------+----------- / / / | +z +z +z | / +Z / . . . | . . . | / . . . yz . | -Z -Z -Z | . -z . . yz . | . . . | +Z -z . . . . | . . . | . . . . . . | . . . | / . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 37) . . . | . . . | . . . 38) . . . | . / . | . . . . xy . | . . . | . xz . . xy . | -Z / -Z | . xz . . . . | . . . | . . . . . . | . +Z . | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- . -Z . | . . . | . . . . . . | . / . | . . . / / +Z | / / / | / +Z / . . . | . / . | . . . . -Z . | . . . | . . . . . . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . . | . / . | . . . . yz -Z | . . . | . -z . . yz . | . +Z . | . -z . . . -Z | . . . | . . . . . . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 39) . . . | . . . | -Z . . 40) . . . | . / . | . . . . xy . | . . . | -Z xz . . xy . | . +Z . | . xz . . . . | . . . | -Z . . . . . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . -Z . . . . | . / . | . . . / +Z / | / / / | +Z / / . . . | . / . | . . . . . . | . . . | . -Z . . . . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . -Z -Z -Z | . +Z . | . . . . yz . | . . . | . -z . . yz . | -Z / -Z | . -z . . . . | . . . | . . . . . . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- ERI --------------+-------------+----------- --------------+-------------+----------- 41) . . . | . . . | . . . 42) . . . | / +z / | . . . . xy . | . . . | . xz . . xy . | / -Z / | . xz . . . . | . . . | . . . . . . | +z +z +z | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- / / +z | . . . | / +z / . . . | . . . | . . . +z -Z +z | . . . | +z +z +z . . . | . . . | . . . / / +z | . . . | / +z / . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . . | / +z / | . . . . yz -Z | . . . | . -z . . yz . | +z +z +z | . -z . . . -Z | . . . | . . . . . . | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 43) . . . | . . . | -Z . . 44) . . . | / +z / | . . . . xy . | . . . | -Z xz . . xy . | +z +z +z | . xz . . . . | . . . | -Z . . . . . | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- / +z / | . . . | +z / / . . . | . . . | . . . +z +z +z | . . . | +z -Z +z . . . | . . . | . . . / +z / | . . . | +z / / . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . -Z -Z -Z | +z +z +z | . . . . yz . | . . . | . -z . . yz . | / -Z / | . -z . . . . | . . . | . . . . . . | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- Line --------------+-------------+----------- --------------+-------------+----------- 45) . . . | . . . | . . . 46) . . . | . / . | . . . . xy . | . . . | . xz . . xy . | . / . | . xz . . . . | . . . | . . . . . . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . / . | . . . / / / | / +Z / | / +Z / . . . | . +Z . | . -Z . . . . | . . . | . . . . . . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . / . | . . . . yz . | . -Z . | . -z . . yz . | . +Z . | . -z . . . . | . . . | . . . . . . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 47) . . . | . . . | . . . 48) . . . | . / . | . . . . xy . | . -Z . | . xz . . xy . | . +Z . | . xz . . . . | . . . | . . . . . . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . / . | . . . / +Z / | / +Z / | / / / . -Z . | . +Z . | . . . . . . | . . . | . . . . . . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . / . | . . . . yz . | . . . | . -z . . yz . | . / . | . -z . . . . | . . . | . . . . . . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- ERI --------------+-------------+----------- --------------+-------------+----------- 49) . . . | . . . | . . . 50) . . . | . . . | . . . . xy . | . . . | . xz . . xy . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | / +z / | / +z / . . . | / +z / | . . . . . . | +z +z +z | +z +z +z . . . | +z +z +z | . -Z . . . . | / +z / | / +z / . . . | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | / +z / | . . . . yz . | . -Z . | . -z . . yz . | +z +z +z | . -z . . . . | . . . | . . . . . . | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 51) . . . | . . . | . . . 52) . . . | / +z / | . . . . xy . | . -Z . | . xz . . xy . | +z +z +z | . xz . . . . | . . . | . . . . . . | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- / +z / | / +z / | . . . . . . | / +z / | . . . +z +z +z | +z +z +z | . . . . -Z . | +z +z +z | . . . / +z / | / +z / | . . . . . . | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . . . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line Ring --------------+-------------+----------- --------------+-------------+----------- 53) . -YZ . | . . . | . -Z . 54) . -Y . | . / . | . . . -X xy -X | -X -X -X | -X xz -X -XZ xy -XZ |-XZ +Z-X -XZ | -XZ xz -XZ . -YZ . | . . . | . -Z . . -Y . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- . -YZ . | . . . | . -Z . . -Y . | . / . | . . . / +Z-Y / | / / / | / +Z / . -Y . | . / . | . . . . -YZ . | . . . | . -Z . . -Y . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- . -YZ . | . . . | . -Z . . -Y . | . / . | . . . . yz . | . . . | . -z . -Z yz -Z | -Z +Z -Z | -Z -z -Z . -YZ . | . . . | . -Z . . -Y . | . / . | . . . --------------+-------------+----------- --------------+-------------+----------- ERI Ring --------------+-------------+----------- --------------+-------------+----------- 55) . -YZ . | . . . | . -Z . 56) . -Y . | / +z / | . . . -X xy -X | -X -X -X | -X xz -X -XZ xy -XZ |+z-X -XZ +z-X| -XZ xz -XZ . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- / +z-Y / | . . . | / +z / . -Y . | . -Z . | . . . +z -YZ +z | -Z -Z -Z | +z -Z +z . -Y . | . -Z . | . . . / +z-Y / | . . . | / +z / . -Y . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . . yz . | . . . | . -z . -Z yz -Z | +z -Z +z | -Z -z -Z . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 57) / +z-Y / | . . . | . . . 58) . -Y . | . . . | . -Z . +z-X xy +z-X | -XZ -XZ -XZ | -XZ xz -XZ -X xy -X | -X -X -X | -X xz -X / +z-Y / | . . . | . . . . -Y . | . . . | . -Z . --------------+-------------+----------- --------------+-------------+----------- . -YZ . | . . . | . . . . -Y . | . . . | . -Z . . -YZ . | . . . | . . . . -Y . | . . . | . -Z . . -YZ . | . . . | . . . . -Y . | . . . | . -Z . --------------+-------------+----------- --------------+-------------+----------- . -YZ . | . . . | . . . . -Y . | . . . | / +z / . yz . | . . . | . -z . -Z yz -Z | -Z -Z -Z | +z -z +z . -YZ . | . . . | . . . . -Y . | . . . | / +z / --------------+-------------+----------- --------------+-------------+-----------

B) XY-Wing Type 2 Transport (Box-Line wise):-

Hidden Text: Show

Code: Select all: Line Box --------------+-------------+----------- --------------+-------------+----------- 01)-z xy -z | . . xz | . . . 02)-z xyz -z | . . xz | +z +z +z -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | +z +z +z +z +z yz | -z -z -z | / / / . . yz | . . . | / / / --------------+-------------+----------- --------------+-------------+----------- Line Box --------------+-------------+----------- --------------+-------------+----------- 03)-z xy -z | +z xz +z | / / / 04)-z xy -z | . xz . | / / / . . . | -Z -Z -Z | . . . . . . | -Z -Z -Z | +z +z +z . . yz | -z -z -z | . . . . . yz | -z -z -z | +z +z +z --------------+-------------+----------- --------------+-------------+----------- Line Box --------------+-------------+----------- --------------+-------------+----------- 05)-z xy -z | . xz . | . . . 06)-z xy -z | . xz . | . . . / / / | +z +z +z | +z +z +z / / / | . . . | . . . . . yz | -z -z -z | -Z -Z -Z +z +z yz | -z -z -z | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- Line Box --------------+-------------+----------- --------------+-------------+----------- 07)-z xy -z | . xz . | -Z -Z -Z 08)-z xy -z | +z xz +z | -Z -Z -Z +z +z +z | / / / | +z +z +z . . . | / / / | . . . . . yz | -z -z -z | . . . . . yz | -z -z -z | . . . --------------+-------------+----------- --------------+-------------+----------- Line Ring Box Ring --------------+-------------+----------- --------------+-------------+----------- 09)-XYz xy -XYz | -XZ xz -XZ | -X -X -X 10)-XYz xy -XYz | -XZ xz -XZ |+z-X +z-X +z-X +z-Y +z-Y +z-Y| +z +z +z | / / / -Y -Y -Y | . . . | / / / -YZ -YZ yz | -z -z -z | . . . -YZ -YZ yz | -z -z -z | +z +z +z --------------+-------------+----------- --------------+-------------+----------- Line Reduced Ring --------------+-------------+----------- --------------+-------------+----------- 11)-XYz xy -XYz | -XZ xz -XZ | -X -X -X 12)-XYz xy -XYz | -XZ xz -XZ | -X -X -X /-Y /-Y +Z-Y | +z +z +z | / / / +z-Y +z-Y +z-Y| / +Z / | / / / -YZ -YZ yz | -z -z -z | . . . -YZ -YZ yz | -z -z -z | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 13)-XYz xy -XYz | -XZ xz -XZ | -X -X -X /-Y /-Y +Z-Y | / +Z / | / / / -YZ -YZ yz | -z -z -z | . . . --------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- Line Ring ERI Ring --------------+-------------+----------- --------------+-------------+----------- 14)-XYz xy -XYz | -X xz -X | -X -X -X 15)-XYz xy -XYz | -X xz -X | -X -X -X -Y -Y -YZ | . -Z . | . . . -Y -Y -YZ | . -Z . | . . . -Y -Y yz | -z -z -z | . . . -Y -Y yz | -z -z -z | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . -Z . | . . . / / +z | / +z / | . . . / / +Z | / +Z / | / / / +z +z -Z | +z -Z +z | -Z -Z -Z . . -Z | . -Z . | . . . / / +z | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 16)-z xy -z | . xz . | . -Z . 17)-z xy -z | . xz . | . -Z . . . . | . . . | . . . . . . | . . . | . . . . . yz | -z -z -z | . . . . . yz | -z -z -z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . / / +z | . . . | / +z / / / +Z | / / / | / +Z / +z +z +z | . -Z . | +z +z +z . . . | . . . | . . . / / +z | . . . | / +z / --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 18)-z xy -z | . xz . | . . . 19)-z xy -z | . xz . | . . . . . . | . . . | . . . . . . | . . . | . . . . . yz | -z -z -z | . -Z . . . yz | -z -z -z | . -Z . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | / +z / | / +z / / / / | / +Z / | / +Z / . . -Z | +z +z +z | +z +z +z . . . | . . . | . . . . . . | / +z / | / +z / --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 20)-z xy -z | . xz -Z | . . . 21)-z xy -z | . xz -Z | . . . . . . | . . -Z | . . . . . . | . . -Z | . . . . . yz | -z -z -z | . . . . . yz | -z -z -z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . -Z . | . . . / / +z | / / +z | . . . / / +Z | / / +Z | / / / +z +z +z | +z -Z +z | . . . . . . | . -Z . | . . . / / +z | / / +z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 22)-z xy -z | . xz . | . . . 23)-z xy -z | . xz . | . . . . -Z . | . . . | . . . . -Z . | . . . | . . . . -Z yz | -z -z -z | . . . . -Z yz | -z -z -z | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . / +z / | / +z / | . . . / +Z / | / +Z / | / / / +z +z -Z | +z +z +z | . . . . . -Z | . . . | . . . / +z / | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- ERI --------------+-------------+----------- --------------+-------------+----------- 24)-z xy -z | . xz . | . . . 25)-z xy -z | . xz . | . . . . . . | . . . | . . . . . . | . . . | . . . . . yz | -z -z -z | . . . . . yz | -z -z -z | . . . --------------+-------------+----------- --------------+-------------+----------- / / +z | . . . | . . . . . . | . +z . | . . . +z +z +z | . -Z . | . . . . . -Z | +z +z +z | . . . / / +z | . . . | . . . . . . | . +z . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+-----------

C) XYZ-Wing Transport (Box-Line wise):-

Hidden Text: Show

Code: Select all: Line Box --------------+-------------+----------- --------------+-------------+----------- 01)-z xyz -z | . xz . | . . . 02)-z xyz -z | . xz . | +z +z +z -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | +z +z +z +z +z yz | +z +z +z | / / / . . yz | . . . | / / / --------------+-------------+----------- --------------+-------------+----------- Line Ring Box Ring --------------+-------------+----------- --------------+-------------+----------- 03)-XYz xyz -XYz| -XZ xz -XZ | -X -X -X 04)-XYz xyz -XYz| -XZ xz -XZ |+z-X +z-X +z-X +z-Y +z-Y +z-Y| +z +z +z | / / / -Y -Y -Y | . . . | / / / -YZ -YZ yz | -Z -Z -Z | . . . -YZ -YZ yz | -Z -Z -Z | +z +z +z --------------+-------------+----------- --------------+-------------+----------- Line Reduced Ring --------------+-------------+----------- --------------+-------------+----------- 05)-XYz -XYz xyz| -XZ xz -XZ | -X -X -X 06)-XYz xyz -XYz| -XZ xz -XZ | -X -X -X /-Y /-Y +Z-Y| +z +z +z | / / / +z-Y +z-Y +z-Y| / +Z / | / / / -YZ -YZ yz | -Z -Z -Z | . . . -YZ -YZ yz | -Z -Z -Z | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 07)-XYz -XYz xyz| -XZ xz -XZ | -X -X -X /-Y /-Y +Z-Y| / +Z / | / / / -YZ -YZ yz | -Z -Z -Z | . . . --------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- Line Ring ERI Ring --------------+-------------+----------- --------------+-------------+----------- 08)-XYz xyz -XYz| -X xz -X | -X -X -X 09)-XYz xyz -XYz| -XZ xz -XZ | -X -X -X -Y -Y -YZ | . . . | . . . -Y -Y -YZ | . . . | . . . -Y -Y yz | . . . | . . . -Y -Y yz | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . / / +z | / +z / | . . . / / +Z | / +Z / | / / / +z +z +z | +z +z +z | . . . . . . | . . . | . . . / / +z | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line Ring ERI Ring --------------+-------------+----------- --------------+-------------+----------- 10)-XYz -XYz xyz| -X xz -X | -X -X -X 11)-XYz -XYz xyz| -XZ xz -XZ | -X -X -X -Y -Y -YZ | . -Z . | . . . -Y -Y -YZ | . -Z . | . . . -Y -Y yz | . -Z . | . . . -Y -Y yz | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . -Z . | . . . / / +z | / +z / | . . . / / +Z | / +Z / | / / / +z +z -Z | +z -Z +z | -Z -Z -Z . . -Z | . -Z . | . . . / / +z | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- Line --------------+-------------+----------- 12)-z xyz -z | . xz . | . -Z . . . . | . . . | . . . . . yz | . . . | . . . --------------+-------------+----------- . . . | . . . | . . . / / +Z | / / / | / +Z / . . . | . . . | . . . --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- ERI --------------+-------------+----------- --------------+-------------+----------- 13)-z xyz -z | . xz . | . -Z . 14)-z -z xyz | . xz . | . -Z . . . . | . . . | . . . . . . | . . . | . . . . . yz | . . . | . . . . . yz | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- / / +z | . . . | / +z / / / +z | . . . | / +z / +z +z +z | . . . | +z +z +z +z +z +z | . -Z . | +z +z +z / / +z | . . . | / +z / / / +z | . . . | / +z / --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 15)-z xyz -z | . xz -Z | . . . 16)-z xyz -z | . xz -Z | . . . . . . | . . . | . . . . . . | . . . | . . . . . yz | . . . | . . . . . yz | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . / / +z | / / +z | . . . / / +Z | / / +Z | / / / +z +z +z | +z +z +z | . . . . . . | . . . | . . . / / +z | / / +z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 17)-z -z xyz | . xz -Z | . . . 18)-z -z xyz | . xz -Z | . . . . . . | . . -Z | . . . . . . | . . -Z | . . . . . yz | . . -Z | . . . . . yz | . . -Z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . -Z . | . . . / / +z | / / +z | . . . / / +Z | / / +Z | / / / +z +z +z | +z -Z +z | . . . . . . | . -Z . | . . . / / +z | / / +z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 19)-z xyz -z | . xz . | . . . 20)-z xyz -z | . xz . | . . . . -Z . | . . . | . . . . -Z . | . . . | . . . . -Z yz | . . . | . . . . -Z yz | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . / +z / | / +z / | . . . / +Z / | / +Z / | / / / +z +z +z | +z +z +z | . . . . . . | . . . | . . . / +z / | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 21)-z -z xyz | . xz . | . . . 22)-z -z xyz | . xz . | . . . . -Z . | . . . | . . . . -Z . | . . . | . . . . -Z yz | . . . | . . . . -Z yz | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . / +z / | / +z / | . . . / +Z / | / +Z / | / / / +z +z -Z | +z +z +z | . . . . . -Z | . . . | . . . / +z / | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- ERI --------------+-------------+----------- --------------+-------------+----------- 23)-z -z xyz | . xz . | . . . 24)-z -z xyz | . xz . | . . . . . . | . . . | . . . . . . | . . . | . . . . . yz | . . . | . . . . . yz | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- / / +z | . . . | . . . . . . | . +z . | . . . +z +z +z | . -Z . | . . . . . -Z | +z +z +z | . . . / / +z | . . . | . . . . . . | . +z . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+-----------

D) WXYZ-Wing Type 1 Transport Row-Column wise:-

Hidden Text: Show

Code: Select all: --------------+-------------+----------- --------------+-------------+----------- 01) . . . | . . . | / +z / 02) . . . | . . . | . . . . wxy . | xy yz . | +z +z +z . wxy . | xy yz . | . . . . . . | . . . | / +z / . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . / +z / | . . . | . . . . . . | . . . | . . . +z +z +z | . -Z . | . . . . . . | . . . | . . . / +z / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . wz . | . -z . | . -Z . . wz . | . -z . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 03) . . . | / +z / | . . . 04) . . . | . . . | . . . . wxy . | xy +z +z | . yz . . wxy . | xy . . | . yz . . . . | / +z / | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . / +z / | . . . | . . . . . . | . . . | . . . +z +z +z | . . . | . -Z . . . . | . . . | . . . / +z / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . wz . | . -Z . | . -z . . wz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 05) . . . | . . . | / +z / 06) . . . | . . . | . . . . wxy . | xy xyz . | +z +z +z . wxy . | xy xyz . | . . . . . . | . . . | / +z / . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . / +z / | . . . | . . . . . . | . . . | . . . +z +z +z | . -Z . | . . . . . . | . . . | . . . / +z / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . wz . | . -z . | . -Z . . wz . | . -z . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 07) . . . | / +z / | . . . 08) . . . | . . . | . . . . wxy . | xy +z +z | . xyz . . wxy . | xy . . | . xyz . . . . | / +z / | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . / +z / | . . . | . . . . . . | . . . | . . . +z +z +z | . . . | . -Z . . . . | . . . | . . . / +z / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . wz . | . -Z . | . -z . . wz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 09) . . . | . . . | . . . 10) . . / | . . . | . . . . wxy . | xy yz . | . . . . wxy / | xy yz . | . . . / / / | +z +z +z | / +Z / . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . +Z | . -Z . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . +z | . . . | . . . . wz . | . -z . | . -Z . . wz +z | . -z . | . . . . . . | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 11) . . . | . . . | . . . 12) . . / | . . . | . . . . wxy . | xy . . | . yz . . wxy / | xy . . | . yz . / / / | / +Z / | +z +z +z . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . +Z | . . . | . -Z . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . +z | . . . | . . . . wz . | . -Z . | . -z . . wz +z | . . . | . -z . . . . | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 13) . . . | . . . | . . . 14) . . / | . . . | . . . . wxy . | xy xyz . | . . . . wxy / | xy xyz . | . . . / / / | +z +z +z | / +Z / . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . +Z | . -Z . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . +z | . . . | . . . . wz . | . -z . | . -Z . . wz +z | . -z . | . . . . . . | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 15) . . . | . . . | . . . 16) . . / | . . . | . . . . wxy . | xy . . | . xyz . . wxy / | xy . . | . xyz . / / / | / +Z / | +z +z +z . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . +Z | . . . | . -Z . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . +z | . . . | . . . . wz . | . -Z . | . -z . . wz +z | . . . | . -z . . . . | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 17) . -Z . | . . . | . . . 18) . . / | . . . | . . . . wxy . | xy yz . | . . . -Z wxy / | xy yz . | . . . / / +Z | +z +z +z | / / / . . +Z | -Z -Z -Z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . +z | . . . | . . . . wz -Z | . -z . | . . . . wz +z | . -z . | . . . . . -Z | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 19) . -Z . | . . . | . . . 20) . . / | . . . | . . . . wxy . | xy . . | . yz . -Z wxy / | xy . . | . yz . / / +Z | / / / | +z +z +z . . +Z | . . . | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . +z | . . . | . . . . wz -Z | . . . | . -z . . wz +z | . . . | . -z . . . -Z | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 21) . -Z . | . . . | . . . 22) . . / | . . . | . . . . wxy . | xy xyz . | . . . -Z wxy . | xy xyz . | . . . / . +Z | +z +z +z | / / / . . +Z | -Z -Z -Z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . +z | . . . | . . . . wz -Z | . -z . | . . . . wz +z | . -z . | . . . . . -Z | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 23) . -Z . | . . . | . . . 24) . . / | . . . | . . . . wxy . | xy . . | . xyz . -Z wxy / | xy . . | . xyz . / / +Z | / / / | +z +z +z . . +Z | . . . | -Z -Z -Z --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . +z | . . . | . . . . wz -Z | . . . | . -z . . wz +z | . . . | . -z . . . -Z | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 25) . -Z . | . . . | +z +z +z 26) . . . | . . . | . . . . wxy . | xy yz . | +z +z +z -Z wxy . | xy yz . | . . . . . . | . . . | / / / . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . wz . | . -z . | . . . . wz . | . -z . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 27) . -Z . | +z +z +z | . . . 28) . . . | . . . | . . . . wxy . | xy +z +z | . yz . -Z wxy . | xy . . | . yz . . . . | / / / | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . wz . | . . . | . -z . . wz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 29) . -Z . | . . . | +z +z +z 30) . . . | . . . | . . . . wxy . | xy xyz . | +z +z +z -Z wxy . | xy xyz . | . . . . . . | . . . | / / / . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . wz . | . -z . | . . . . wz . | . -z . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 31) . -Z . | +z +z +z | . . . 32) . . . | . . . | . . . . wxy . | xy +z +z | . xyz . -Z wxy . | xy . . | . xyz . . . . | / / / | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . wz . | . . . | . -z . . wz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 33) . -Z . | . . . | . . . 34) . . +z | . . . | . . . . wxy . | xy yz . | . . . -Z wxy +z | xy yz . | . . . +z +z +z | +z +z +z | / / / . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . +z | . . . | . . . . wz . | . -z . | . . . . wz +z | . -z . | . . . . . . | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 35) . -Z . | . . . | . . . 36) . . +z | . . . | . . . . wxy . | xy . . | . yz . -Z wxy +z | xy . . | . yz . +z +z +z | / / / | +z +z +z . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . +z | . . . | . . . . wz . | . . . | . -z . . wz +z | . . . | . -z . . . . | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 37) . -Z . | . . . | . . . 38) . . +z | . . . | . . . . wxy . | xy xyz . | . . . -Z wxy +z | xy xyz . | . . . +z +z +z | +z +z +z | / / / . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . +z | . . . | . . . . wz . | . -z . | . . . . wz +z | . -z . | . . . . . . | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 39) . -Z . | . . . | . . . 40) . . +z | . . . | . . . . wxy . | xy . . | . xyz . -Z wxy +z | xy . . | . xyz . +z +z +z | / / / | +z +z +z . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . +z | . . . | . . . . wz . | . . . | . -z . . wz +z | . . . | . -z . . . . | . . . | . . . . . +z | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 41) . . . | . . . | . / . 42) . -Z . | . -Z . | . . . -Z wxy -Z | xy yz -Z | -Z +Z -Z . wxy . | xy yz . | . . . . . . | . . . | . / . . -Z . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . / . . -Z . | . . . | . . . . . . | . . . | . / . / +Z / | / +Z / | / / / . . . | . . . | . / . . -Z . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . / . . -Z . | . -Z . | . . . -Z wz -Z | -Z -z -Z | -Z +Z -Z . wz . | . -z . | . . . . . . | . . . | . / . . -Z . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 43) . . . | . / . | . . . 44) . -Z . | . . . | . -Z . -Z wxy -Z | xy +Z -Z | -Z yz -Z . wxy . | xy . . | . yz . . . . | . / . | . . . . -Z . | . . . | . -Z . --------------+-------------+----------- --------------+-------------+----------- . . . | . / . | . . . . -Z . | . . . | . -Z . . . . | . / . | . . . / +Z / | / / / | / +Z / . . . | . / . | . . . . -Z . | . . . | . -Z . --------------+-------------+----------- --------------+-------------+----------- . . . | . / . | . . . . -Z . | . . . | . -Z . -Z wz -Z | -Z +Z -Z | -Z -z -Z . wz . | . . . | . -z . . . . | . / . | . . . . -Z . | . . . | . -Z . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 45) . . . | . . . | . / . 46) . -Z . | . -Z . | . . . -Z wxy -Z | xy xyz -Z | -Z +Z -Z . wxy . | xy xyz . | . . . . . . | . . . | . / . . -Z . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . / . . -Z . | . . . | . . . . . . | . . . | . / . / +Z / | / +Z / | / / / . . . | . . . | . / . . -Z . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . / . . -Z . | . -Z . | . . . -Z wz -Z | -Z -z -Z | -Z +Z -Z . wz . | . -z . | . . . . . . | . . . | . / . . -Z . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 47) . . . | . / . | . . . 48) . -Z . | . . . | . -Z . -Z wxy -Z | xy +Z -Z | -Z xyz -Z . wxy . | xy . . | . xyz . . . . | . / . | . . . . -Z . | . . . | . -Z . --------------+-------------+----------- --------------+-------------+----------- . . . | . / . | . . . . -Z . | . . . | . -Z . . . . | . / . | . . . / +Z / | / / / | / +Z / . . . | . / . | . . . . -Z . | . . . | . -Z . --------------+-------------+----------- --------------+-------------+----------- . . . | . / . | . . . . -Z . | . . . | . -Z . -Z wz -Z | -Z +Z -Z | -Z -z -Z . wz . | . . . | . -z . . . . | . / . | . . . . -Z . | . . . | . -Z . --------------+-------------+----------- --------------+-------------+-----------

E) WXYZ-Wing Type 2a Transport Box-Line wise:-

Hidden Text: Show

Code: Select all: --------------+-------------+----------- --------------+-------------+----------- 01)-Z wz -Z | -z -z -z | +z +z +z 02)-Z wz -Z | -z -z -z | . . . -z wxy -z | -Z xz yz | +z +z +z -z wxy -z | -Z xz yz | . . . . . . | . . . | / / / +z +z +z | +z +z +z | / / / --------------+-------------+----------- --------------+-------------+----------- 03)-Z xz yz | -z -z -z | +z +z +z 04)-Z xz yz | -z -z -z | . . . -z wxy -z | -Z wz -Z | +z +z +z -z wxy -z | -Z wz -Z | . . . . . . | . . . | / / / +z +z +z | +z +z +z | / / / --------------+-------------+----------- --------------+-------------+----------- 05)-Z wz -Z | -z -z -z | +z +z +z 06)-Z wz -Z | -z -z -z | . . . -z wxy -z | -Z xy yz | +z +z +z -z wxy -z | -Z xy yz | . . . . . . | . . . | / / / +z +z +z | +z +z +z | / / / --------------+-------------+----------- --------------+-------------+----------- 07)-Z xy yz | -z -z -z | +z +z +z 08)-Z xy yz | -z -z -z | . . . -z wxy -z | -Z wz -Z | +z +z +z -z wxy -z | -Z wz -Z | . . . . . . | . . . | / / / +z +z +z | +z +z +z | / / / --------------+-------------+----------- --------------+-------------+----------- 09)-Z wz -Z | +z +z +z | -z -z -z 10)-Z wz -Z | . . . | -z -z -z -z wxy -z | +z xy +z | -Z yz -Z -z wxy -z | . xy . | -Z yz -Z . . . | / / / | . . . +z +z +z | / / / | +z +z +z --------------+-------------+----------- --------------+-------------+----------- 11) . xy . | . . . | / / / 12)+z xy +z | +z +z +z | / / / -z wxy -z | -Z wz -Z | +z +z +z -z wxy -z | -Z wz -Z | . . . -Z -Z yz | -z -z -z | +z +z +z -Z -Z yz | -z -z -z | . . . --------------+-------------+----------- --------------+-------------+----------- 13)-Z wz -Z | -z -z -z | +z +z +z 14)-Z wz -Z | -z -z -z | . . . -z wxy -z | -Z xy xyz | +z +z +z -z wxy -z | -Z xy xyz | . . . . . . | . . . | / / / +z +z +z | +z +z +z | / / / --------------+-------------+----------- --------------+-------------+----------- 15)-Z xy xyz | -z -z -z | +z +z +z 16)-Z xy xyz | -z -z -z | . . . -z wxy -z | -Z wz -Z | +z +z +z -z wxy -z | -Z wz -Z | . . . . . . | . . . | / / / +z +z +z | +z +z +z | / / / --------------+-------------+----------- --------------+-------------+----------- 17)-Z wz -Z | +z +z +z | -z -z -z 18)-Z wz -Z | . . . | -z -z -z -z wxy -z | +z xy +z | -Z xyz -Z -z wxy -z | . xy . | -Z xyz -Z . . . | / / / | . . . +z +z +z | / / / | +z +z +z --------------+-------------+----------- --------------+-------------+----------- 19) . xy . | . . . | / / / 20)+z xy +z | +z +z +z | / / / -z wxy -z | -Z wz -Z | +z +z +z -z wxy -z | -Z wz -Z | . . . -Z -Z xyz | -z -z -z | +z +z +z -Z -Z xyz | -z -z -z | . . . --------------+-------------+----------- --------------+-------------+----------- 21)-Z wz -Z | -z -z -z | +z +z +z 22)-Z wz -Z | -z -z -z | . . . -z wxy -z | -Z xz xyz | +z +z +z -z wxy -z | -Z xz xyz | . . . . . . | . . . | / / / +z +z +z | +z +z +z | / / / --------------+-------------+----------- --------------+-------------+----------- 23)-Z xz xyz | -z -z -z | +z +z +z 24)-Z xz xyz | -z -z -z | . . . -z wxy -z | -Z wz -Z | +z +z +z -z wxy -z | -Z wz -Z | . . . . . . | . . . | / / / +z +z +z | +z +z +z | / / / --------------+-------------+----------- --------------+-------------+----------- 25)-Z wz -Z | -z -z -z | +z +z +z 26)-Z wz -Z | -z -z -z | . . . -z wxy -z | -Z xyz xyz | +z +z +z -z wxy -z | -Z xyz xyz | . . . . . . | . . . | / / / +z +z +z | +z +z +z | / / / --------------+-------------+----------- --------------+-------------+----------- 27)-Z xyz xyz | -z -z -z | +z +z +z 28)-Z xyz xyz | -z -z -z | . . . -z wxy -z | -Z wz -Z | +z +z +z -z wxy -z | -Z wz -Z | . . . . . . | . . . | / / / +z +z +z | +z +z +z | / / / --------------+-------------+----------- --------------+-------------+-----------

F) WXYZ-Wing Type 2b Transport Box-Line wise:-

Hidden Text: Show

G) WXYZ-Wing Type 3 Transport Box-Line wise:-

Hidden Text: Show

Code: Select all: --------------+-------------+----------- 01)-Z wz -Z | -Z -Z -Z | . . . -z wxyz -z | -Z xz yz | . . . . . . | . . . | / / / --------------+-------------+----------- 02)-Z xz yz | -Z -Z -Z | . . . -z wxyz -z | -Z wz -Z | . . . . . . | . . . | / / / --------------+-------------+----------- 03) . xz . | . . . | / / / -z wxyz -z | -Z wz -Z | . . . -Z -Z yz | -Z -Z -Z | . . . --------------+-------------+----------- 04)-Z xz -Z | -Z -Z -Z | . . . -z wxyz -z | . wz . | / / / -Z -Z yz | -Z -Z -Z | . . . --------------+-------------+----------- 05)-Z xz -Z | -Z -Z -Z | . . . -z wxyz -z | -Z wz -Z | . . . . . yz | . . . | / / / --------------+-------------+----------- 06)-Z wz -Z | -Z -Z -Z | . . . -z wxyz -z | -Z xy yz | . . . . . . | . . . | / / / --------------+-------------+----------- 07)-Z xy yz | -Z -Z -Z | . . . -z wxyz -z | -Z wz -Z | . . . . . . | . . . | / / / --------------+-------------+----------- 08)-Z wz -Z | . . . | -Z -Z -Z -z wxyz -z | . xy . | -Z yz -Z . . . | / / / | . . . --------------+-------------+----------- 09) . xy . | . . . | / / / -z wxyz -z | -Z wz -Z | . . . -Z -Z yz | -Z -Z -Z | . . . --------------+-------------+----------- 10)-Z wz -Z | -Z -Z -Z | . . . -z wxyz -z | -Z xy xyz | . . . . . . | . . . | / / / --------------+-------------+----------- 11)-Z xy xyz | -Z -Z -Z | . . . -z wxyz -z | -Z wz -Z | . . . . . . | . . . | / / / --------------+-------------+----------- 12)-Z wz -Z | . . . | -Z -Z -Z -z wxyz -z | . xy . | -Z xyz -Z . . . | / / / | . . . --------------+-------------+----------- 13) . xy . | . . . | / / / -z wxyz -z | -Z wz -Z | . . . -Z -Z xyz | -Z -Z -Z | . . . --------------+-------------+----------- 14)-Z wz -Z | -Z -Z -Z | . . . -z wxyz -z | . xz xyz | . . . . . . | . . . | / / / --------------+-------------+----------- 15)-Z xz xyz | -Z -Z -Z | . . . -z wxyz -z | -Z wz -Z | . . . . . . | . . . | / / / --------------+-------------+----------- 16) . xz . | . . . | / / / -z wxyz -z | -Z wz -Z | . . . -Z -Z xyz | -Z -Z -Z | . . . --------------+-------------+----------- 17)-Z xz -Z | -Z -Z -Z | . . . -z wxyz -z | . wz . | / / / -Z -Z xyz | -Z -Z -Z | . . . --------------+-------------+----------- 18)-Z xz -Z | -Z -Z -Z | . . . -z wxyz -z | -Z wz -Z | . . . . . xyz | . . . | / / / --------------+-------------+----------- 19)-Z wz -Z | -Z -Z -Z | . . . -z wxyz -z | -Z xyz xyz | . . . . . . | . . . | / / / --------------+-------------+----------- 20)-Z xyz xyz | -Z -Z -Z | . . . -z wxyz -z | -Z wz -Z | . . . . . . | . . . | / / / --------------+-------------+----------- 21) . xyz . | . . . | / / / -z wxyz -z | -Z wz -Z | . . . -Z -Z xyz | -Z -Z -Z | . . . --------------+-------------+----------- 22)-Z xyz -Z | -Z -Z -Z | . . . -z wxyz -z | . wz . | / / / -Z -Z xyz | -Z -Z -Z | . . . --------------+-------------+----------- 23)-Z xyz -Z | -Z -Z -Z | . . . -z wxyz -z | -Z wz -Z | . . . . . xyz | . . . | / / / --------------+-------------+-----------

Note 1: I have used small "-z" for regular wings eliminations and capital "-X", "-Y" and "-Z" for additional Transported eliminations for easy understanding.
Note 2: I have used capital "+Z" for cell that must contain "z" digit and small "+z" for at least one or more cells that may contain "z" digit.
Note 3: I have used slash "/" character for cells that must NOT contain "z" digit.

A 1-58) As per StrmCkr complete exemplars.

B 1-25) As per StrmCkr complete exemplars.

C 1-24) As per StrmCkr complete exemplars.

D 1-48) Need StrmCkr confirmation.

E 1-28) Need StrmCkr confirmation.

F 1-9) Need StrmCkr confirmation.

G 1-23) Need StrmCkr confirmation.

H 1-35) As per StrmCkr complete exemplars.

R. Jamil
------------
In mathematics: a straight line is a special type of a curve.

Whereas, in English: a straight line isn't a curve, and a curve isn't a straight line.

by **StrmCkr** » Sat Feb 18, 2017 7:07 am

missing eliminations: { im pretty sure most of the preliminary ones you listed above are lacking similar eliminations as I've shown here.}
in the first box

Code: Select all: --------------+-------------+----------- 01) -z wz -z | -Z -Z -Z | +z +z +z -z wxyz -z | . xz yz | +z +z +z . . . | . . . | / / /

if the -z is seen by every permutation of placement then its an elimination.
{or transversely, placing any of the z's as true = at least 1 cell with no candidates }

by **StrmCkr** » Sun Mar 12, 2017 4:57 am

I'll toss the examples as requested into my solver.
I wrote it based and utilizing my barn code, so it can do size 1-9 wings easily.
I'll have a look over which ones work or don't and see if it produces any missed eliminations for the exemplars.
Cheers strmckr

by **StrmCkr** » Sun Mar 12, 2017 7:35 am

C) XYZ-Wings Transport Box-Line wise:-

Code: Select all: --------------+-------------+----------- --------------+-------------+----------- 01)-xyz xyz -xyz| -Zx -Zx xz | +z-x +z-x +z-x 02)-xyz xyz -xyz| -Zx -Zx xz| -x -x -x -y -y -y | . . . | / / / +z +z +z | +z +z +z | / / / -yZ -yZ yz | -Z -Z -Z | +z +z +z -yZ -yZ yz | -Z -Z -Z | . . . --------------+-------------+----------- --------------+-------------+-----------

Code: Select all: -----------+-----------+---------- -----------+-----------+---------- -z xyz -z | . -z . | . xz . -z xyz -z | . -z . | . yz . . . . | . . . | . . . . . . | . . . | . . . . . yz | . . . | . . . . . xz | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | . . . / / z | / z / | / / / / / z | / z / | / / / . . . | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: this one bugs my code out as it cant find the loop as all z's aren't found in both C&D sector intersections of T. -----------+-----------+---------- -----------+-----------+---------- -z xyz -z | -x -x -x | -x xz -x -z xyz -z | -x -x -x | . yz . -y -y -yz | . . . | . . . -y -y -yz | . . . | . . . -y -y yz | . . . | . . . -y -y xz | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | . . . / / z | / / / | / z / / / z | / / / | / z / . . . | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

Code: Select all: -----------+-----------+---------- -----------+-----------+---------- -xyz xyz -xyz|-x -x -x | -xz xz -xz z-y xyz -yz | . . . | . . . z-y z-y z-y | / / / | / z / z-y -xyz -yz | . . . | . . . -yz -yz yz | . . . | -z -z -z z-y -xyz yz | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . -z . / -x . | . . . | . . . . . . | . . . | . -z . / -x . | . . . | . . . . . . | . . . | . -z . / -x . | . . . | . . . -----------+-----------+---------- -----------+-----------+---------- . . . | . . . | . -z . / -xz -z | . . . | . . . . . . | . . . | . -z . z xz -z | -z -z -z | -z -z -z . . . | . . . | . -z . / -xz -z | . . . | . . . -----------+-----------+---------- -----------+-----------+----------

by **rjamil** » Mon Nov 25, 2019 5:50 pm

1 of 3
Hi all,

Wish to update above post here, in 3 parts, due reached forum 100,000 characters limit per post. Also including here the updated post of mine too.

Code: Select all: XY-Wing Type 1 Transport (78 exemplars) (Row-Column wise): ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 01) . . . | / +z / | . . . 02) . . . | . . . | . . . . xy . | +z . +z | . xz . . xy . | . . . | . xz . . . . | / +z / | . . . . . . | . . . | . . . 03---------------+---------------+---------------03---------------+---------------+--------------- . . . | . . . | . . . / +z / | . . . | . . . . . . | . . . | . . . +z . +z | . . . | . [-Z] . . . . | . . . | . . . / +z / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . [-Z] . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 03) . . . | . . . | . . . 04) . . . | . . . | . . . . xy . | . [-Z] . | . xz . . xy . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . 03---------------+---------------+---------------03---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | / +z / . . . | . . . | . . . . [-Z] . | . . . | +z . +z . . . | . . . | . . . . . . | . . . | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | / +z / | . . . . . . | . . . | . . . . yz . | +z . +z | . -z . . yz . | . . . | . -z . . . . | / +z / | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Reduced ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 05) . [-Z] . | / +Z / | . . . 06) . . . | . . . | . . . . xy . | +z . +z | . xz . [-Z] xy . | . . . | . xz . . . . | / / / | . . . . . . | . . . | . . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . / +z / | . . . | . . . . . . | . . . | . . . +Z . / | . . . | . -Z . . . . | . . . | . . . / +z / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . -Z . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 07) . . . | . . . | . . . 08) . . . | . . . | . . . . xy . | . -Z . | . xz . . xy . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | / +z / . . . | . . . | . . . . -Z . | . . . | / . +Z . . . | . . . | . . . . . . | . . . | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | / / / | . . . . . . | . . . | . . . . yz . | +z . +z | . -z . . yz . | . . . | . -z [-Z] . . . | / +Z / | . [-Z] . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 09) . . . | / +z / | . . . 10) . . . | . . . | . . . . xy . | +z . +z | . xz . . xy . | . [-Z] . | . xz . . . . | / +z / | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . / +z / | / +z / | . . . . [-Z] . | +z . +z | . . . +z . +z | +z . +z | . -Z . . . . | / +z / | . . . / +z / | / +z / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . -Z . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 11) . . . | . . . | . . . 12) . . . | . . . | . . . . xy . | . -Z . | . xz . . xy . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . . . . | / +z / | / +z / . . . | +z . +z | . [-Z] . . -Z . | +z . +z | +z . +z . . . | / +z / | . . . . . . | / +z / | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | / +z / | . . . . . . | . . . | . . . . yz . | +z . +z | . -z . . yz . | . [-Z] . | . -z . . . . | / +z / | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Reduced ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 13) . [-Z] . | / +Z / | . . . 14) . . . | . . . | . . . . xy . | +z . +z | . xz . [-Z] xy . | . -Z . | . xz . . . . | / / / | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . / +z / | / +z / | . . . . -Z . | +z . +z | . . . +Z . / | +z . +z | . -Z . . . . | / +z / | . . . / +z / | / +z / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . -Z . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 15) . . . | . . . | . . . 16) . . . | . . . | . . . . xy . | . -Z . | . xz . . xy . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . . . . | / +z / | / +z / . . . | +z . +z | . -Z . . -Z . | +z . +z | / . +Z . . . | / +z / | . . . . . . | / +z / | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | / / / | . . . . . . | . . . | . . . . yz . | +z . +z | . -z . . yz . | . -Z . | . -z [-Z] . . . | / +Z / | . [-Z] . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 17) . . . | / +z / | . . . 18) . . . | . . . | . . . . xy . | +z . +z | . xz . . xy . | . -Z . | . xz . . . . | / +z / | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . / +z / | / +Z / | . [-Z] . . -Z . | +Z . / | . . . +z . +z | +z . +z | . -Z . . . . | / +z / | . . . / +z / | / / / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . |[-Z] -Z . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 19) . . . | . . . | . . . 20) . . . | . . . | . . . . xy . | . -Z [-Z] | . xz . . xy . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . . . . | / / / | / +z / . . . | / . +Z | . (-Z) . . -Z . | +z . +z | +z . +z . . . | / +z / | . . . . [-Z] . | / +Z / | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | / +z / | . . . . . . | . . . | . . . . yz . | +z . +z | . -z . . yz . | . (-Z) . | . -z . . . . | / +z / | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Reduced ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 21) . [-Z] . | / +Z / | . . . 22) . . . | . . . | . . . . xy . | +z . +z | . xz . . xy [-Z] | . -Z . | . xz . . . . | / / / | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . / +z / | / +Z / | . -Z . . -Z . | +Z . / | . . . / . +Z | +z . +z | . -Z . . . . | / +z / | . . . / +z / | / / / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | -Z -Z . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 23) . . . | . . . | . . . 24) . . . | . . . | . . . . xy . | . -Z -Z | . xz . . xy . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . . . . | / / / | / +z / . . . | / . +Z | . -Z . . -Z . | +z . +z | / . +Z . . . | / +z / | . . . . -Z . | / +Z / | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | / / / | . . . . . . | . . . | . . . . yz . | +z . +z | . -z . . yz . | . -Z . | . -z [-Z] . . . | / +Z / | . [-Z] . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 25) . . . | / +z / | . . . 26) . . . | . . . |[-Z] . . . xy . | +z . +z | . xz . . xy . | . . . |[-Z] xz . . . . | / +z / | . . . . . . | . . . |[-Z] . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . / +z / | . . . | +z / . . . . | . . . | . . . +z . +z | . . . | . -Z +z . . . | . . . | . . . / +z / | . . . | +z / . ---------------+---------------+--------------- ---------------+---------------+--------------- [-Z] [-Z] [-Z] | +z . +z | . . . . . . | . . . | . . . . yz . | / -Z / | . -z . . yz . | . . . | . -z . . . . | / +z / | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 27) . . . | / +z / | . . . 28) . . . | . . . | . . . . xy . | / -Z / | . xz . . xy . | . . . | . xz . . . . | +z . +z |[-Z] [-Z] [-Z] . . . | . . . | . . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . / / +z | . . . | / +z / . . . | . . . | . . . +z -Z . | . . . | +z . +z . . . | . . . | . . . / / +z | . . . | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | / +z / | . . . . . [-Z] | . . . | . . . . yz . | +z . +z | . -z . . yz [-Z] | . . . | . -z . . . . | / +z / | . . . . . [-Z] | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Reduced ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 29) . [-Z] . | / +Z / | . . . 30) . . . | . . . | -Z . . . xy . | +z . +z | . xz . [-Z] xy . | . . . | -Z xz . . . . | / / / | . . . . . . | . . . | -Z . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . / +z / | . . . | +z / / . . . | . . . | . . . +Z . / | . . . | . -Z +z . . . | . . . | . . . / +z / | . . . | +z / / ---------------+---------------+--------------- ---------------+---------------+--------------- -Z -Z -Z | +z . +z | . . . . . . | . . . | . . . . yz . | / -Z / | . -z . . yz . | . . . | . -z . . . . | / +z / | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 31) . . . | / +z / | . . . 32) . . . | . . . | . . . . xy . | / -Z / | . xz . . xy . | . . . | . xz . . . . | +z . +z | -Z -Z -Z . . . | . . . | . . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . / / +z | . . . | / +z / . . . | . . . | . . . +z -Z . | . . . | / . +Z . . . | . . . | . . . / / +z | . . . | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | / / / | . . . . . -Z | . . . | . . . . yz . | +z . +z | . -z . . yz -Z | . . . | . -z [-Z] . . . | / +Z / | . [-Z] . . . -Z | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Line ---------------+---------------+--------------- ---------------+---------------+--------------- 33) . . . | . / . | . . . 34) . . . | . . . | . . . . xy . | . +Z . | . xz . . xy . | . [-Z] . | . xz . . . . | . / . | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | . / . | . . . . . . | . . . | . . . . [-Z] . | . +Z . | . . . / +Z / | / +Z / | / / / . . . | . / . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . / . | . . . . . . | . . . | . . . . yz . | . / . | . -z . . yz . | . . . | . -z . . . . | . / . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 35) . . . | . / . | . . . 36) . . . | . . . | . . . . xy . | . / . | . xz . . xy . | . . . | . xz . . . . | . / . | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | . / . | . . . . . . | . . . | . . . . . . | . +Z . | . [-Z] . / / / | / +Z / | / +Z / . . . | . / . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . / . | . . . . . . | . . . | . . . . yz . | . +Z . | . -z . . yz . | . [-Z] . | . -z . . . . | . / . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 37) . . . | . / . | . . . 38) . . . | . . . |[-Z] . . . xy . | . +Z . | . xz . . xy . | . . . |[-Z] xz . . . . | . / . | . . . . . . | . . . |[-Z] . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . / . | . . . . . . | . . . | . [-Z] . . . . | . / . | . . . / +Z / | / / / | +Z / / . . . | . / . | . . . . . . | . . . | . [-Z] . ---------------+---------------+--------------- ---------------+---------------+--------------- [-Z] [-Z] [-Z] | . +Z . | . . . . . . | . . . | . . . . yz . |[-Z] / [-Z] | . -z . . yz . | . . . | . -z . . . . | . / . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 39) . . . | . / . | . . . 40) . . . | . . . | . . . . xy . |[-Z] / [-Z] | . xz . . xy . | . . . | . xz . . . . | . +Z . |(-Z) (-Z) (-Z) . . . | . . . | . . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . / . | . . . . [-Z] . | . . . | . . . . . . | . / . | . . . / / +Z | / / / | / +Z / . . . | . / . | . . . . [-Z] . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . / . | . . . . . (-Z) | . . . | . . . . yz . | . +Z . | . -z . . yz (-Z) | . . . | . -z . . . . | . / . | . . . . . (-Z) | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Line Ring ---------------+---------------+--------------- ---------------+---------------+--------------- 41) . -YZ . | . . . | . -Z . 42) . -Y . | . / . | . . . -X xy -X | -X -X -X | -X xz -X -XZ xy -XZ |-XZ +Z-X -XZ | -XZ xz -XZ . -YZ . | . . . | . -Z . . -Y . | . / . | . . . 03---------------+---------------+---------------03---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | . / . | . . . / +Z-Y / | / / / | / +Z / . -Y . | . / . | . . . . -YZ . | . . . | . -Z . . -Y . | . / . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | . / . | . . . . yz . | . . . | . (-z) . -Z yz -Z | -Z +Z -Z | -Z (-z) -Z . -YZ . | . . . | . -Z . . -Y . | . / . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ERI Ring ---------------+---------------+--------------- ---------------+---------------+--------------- 43) . -YZ . | . . . | . -Z . 44) . -Y . | / +z / | . . . -X xy -X | -X -X -X | -X xz -X -XZ xy -XZ |+z-X -XZ +z-X | -XZ xz -XZ . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . 03---------------+---------------+---------------03---------------+---------------+--------------- / +z-Y / | . . . | / +z / . -Y . | . -Z . | . . . +z -YZ +z | -Z -Z -Z | +z -Z +z . -Y . | . -Z . | . . . / +z-Y / | . . . | / +z / . -Y . | . -Z . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . . yz . | . . . | . (-z) . -Z yz -Z | +z -Z +z | -Z (-z) -Z . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 45) / +z-Y / | . . . | . . . 46) . -Y . | . . . | . -Z . +z-X xy +z-X | -XZ -XZ -XZ | -XZ xz -XZ / -X xy -X | -X -X -X | -X xz -X / +z-Y / | . . . | . . . . -Y . | . . . | . -Z . 01---------------+---------------+---------------01---------------+---------------+--------------- . -YZ . | . . . | . . . . -Y . | . . . | . -Z . . -YZ . | . . . | . . . . -Y . | . . . | . -Z . . -YZ . | . . . | . . . . -Y . | . . . | . -Z . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . . . . -Y . | . . . | / +z / . yz . | . . . | . -z . -Z yz -Z | -Z -Z -Z | +z -z +z . -YZ . | . . . | . . . . -Y . | . . . | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 47) / +z / | . . . | . . . 48) / / +z | . . . | . . . / xy / | . . . | . xz . +z xy . | . . . | . xz . +z . +z | . . . |[-Z] [-Z] [-Z] / / +z | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . [-Z] | . . . | . . . . yz . | . . . | . -z . . yz [-Z] | . . . | . -z . . . . | . . . | . . . . . [-Z] | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 49) . . . | . . . |(-Z) . . 50) . . . | . . . | . . . . xy . | . . . |[-Z] xz . . xy . | . . . | . xz . . . . | . . . |(-Z) . . . . . | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | +z / / (-Z) [-Z] (-Z) | . . . | +z . +z . yz . | . . . | . -z +z . yz . | . . . | / -z / . . . | . . . | +z / / . . . | . . . | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- Box ---------------+---------------+--------------- ---------------+---------------+--------------- 51) . [-Z] . | +z +z +z | . . . 52) . . . | . . . | . . . . xy . | +z +z +z | . xz . [-Z] xy . | . . . | . xz . . . . | / / / | . . . . . . | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . . . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 53) . . . | . . . | . . . 54) . . . | . . . | . . . . xy . | . . . | . xz . . xy . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | / +z +z . . . | . . . | . . . . . . | . . . | / +z +z . . . | . . . | . . . . . . | . . . | / +z +z ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | / / / | . . . . . . | . . . | . . . . yz . | +z +z +z | . -z . . yz . | . . . | . -z [-Z] . . . | +z +z +z | . [-Z] . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Line ---------------+---------------+--------------- ---------------+---------------+--------------- 55) . [-Z] . | . . . | . . . 56) . . +z | . . . | . . . . xy . | . . . | . xz . [-Z] xy +z | . . . | . xz . +z +z +z | / / / | +z +z +z . . +z | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . +z | . . . | . . . . yz . | . . . | . -z . . yz +z | . . . | . -z . . . . | . . . | . . . . . +z | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 57) . . . | . . . | . . . 58) . . . | . . . |(+z) . . . xy . | . . . | . xz . . xy . | . . . | +z xz . . . . | . . . | . . . . . . | . . . |(+z) . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- (+z) +z (+z) | / / / | +z +z +z . . . | . . . | +z . . . yz . | . . . | . (-z) . . yz . | . . . | +z (-z) [-Z] . . . | . . . | . [-Z] . . . . | . . . | +z . . ---------------+---------------+--------------- ---------------+---------------+--------------- Reduced Line Ring ---------------+---------------+--------------- ---------------+---------------+--------------- 59) . -YZ . | . . . | -Z -Z -Z 60) . -Y / | . . . | . . . -X xy -X | -X -X -X | -XZ xz -XZ -XZ xy +Z-X | -XZ -XZ -XZ | -XZ xz -XZ / +Z-Y / | / / / | +z +z +z . -Y / | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . -YZ . | . . . | . . . . -Y / | . . . | . . . . -YZ . | . . . | . . . . -Y / | . . . | . . . . -YZ . | . . . | . . . . -Y / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . . . -Z -YZ +z | . . . | . . . . yz . | . . . | . -z . -Z yz +z | . . . | . -z . . -YZ . | . . . | . . . -Z -YZ +z | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- 15 ---------------+---------------+--------------- ---------------+---------------+--------------- 61) . -Y . | . . . | . -Z . 62) . -Y . | . . . | +z (-Z) (-Z) -X xy -X | -X -X -X | -X xz -X -X xy -X | -X -X -X |+z-X xz -X . -Y . | . . . | . -Z . . -Y . | . . . | +z (-Z) (-Z) 02---------------+---------------+---------------02---------------+---------------+--------------- . -Y . | . . . | . -Z . . -Y . | . . . | / . . . -Y . | . . . | . -Z . . -Y . | . . . | / . . . -Y . | . . . | . -Z . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- (+z) +z-Y (+z) | / / / | / +Z / . -Y . | . . . | / . . (-Z) yz (-Z) | . . . | . -z . -Z yz -Z | -Z -Z -Z | +Z -z -Z (-Z) -YZ (-Z) | . . . | . -Z . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 63) . -YZ . | . . . | -Z -Z -Z 64) . -Y / | . . . | . . . -X xy -X | -X -X -X | -XZ xz -XZ -XZ xy +Z-X | -XZ -XZ -XZ | -XZ xz -XZ / +Z-Y / | / / / | / +Z / . -Y / | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y / | . . . | . . . . -YZ . | . . . | . -Z . . -Y / | . . . | . . . . -YZ . | . . . | . -Z . . -Y / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . -Z . -Z -YZ / | . . . | . . . . yz . | . . . | . (-z) . -Z yz +Z | -Z -Z -Z | -Z (-z) -Z . -YZ . | . . . | . -Z . -Z -YZ / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 65) . -YZ . | . . . | . -Z . 66) . -Y . | . . . | / (-Z) (-Z) -X xy -X | -X -X -X | -X xz -X -XZ xy -XZ | -XZ -XZ -XZ |+Z-X xz -XZ . -YZ . | . . . | . -Z . . -Y . | . . . | / (-Z) (-Z) 02---------------+---------------+---------------02---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | . . . | / . . . -YZ . | . . . | . -Z . . -Y . | . . . | / . . . -YZ . | . . . | . -Z . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- / +Z-Y / | / / / | / +Z / . -Y . | . . . | / . . (-Z) yz (-Z) | . . . | . (-z) . -Z yz -Z | -Z -Z -Z | +Z (-z) -Z (-Z) -YZ (-Z) | . . . | . -Z . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- Line ---------------+---------------+--------------- ---------------+---------------+--------------- 67) . -Z . | . . . | . . . 68) . . / | . . . | . . . . xy . | . . . | . xz . -Z xy / | . . . | . xz . / / +Z | / / / | +z +z +z . . +Z | . . . |[-Z] [-Z] [-Z] 04---------------+---------------+---------------04---------------+---------------+--------------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . [-Z] | . . . | . . . . . +z | . . . | . . . . yz [-Z] | . . . | . -z . . yz +z | . . . | . -z . . . [-Z] | . . . | . . . . . +z | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 69) . . . | . . . |(-Z) . . 70) . . . | . . . |(+z) . . . xy . | . . . |[-Z] xz . . xy . | . . . | +z xz . . . . | . . . |(-Z) . . . . . | . . . |(+z) . . 04---------------+---------------+---------------04---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- (+z) +z (+z) | / / / | +Z / / (-Z) [-Z] (-Z)| . . . | +Z . . . yz . | . . . | . -z . . yz . | . . . | / -z -Z . . . | . . . | . -Z . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 71) . . . | . . . | . . . 72) . . / | . . . | . . . . xy . | . . . | . xz . . xy / | . . . | . xz . / / / | / +Z / | +z +z +z . . / | . . . | . . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . +Z | . . . | . [-Z] . . . . | . . . | . . . . . / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . +z | . . . | . . . . yz . | . [-Z] . | . -z . . yz +z | . . . | . -z . . . . | . . . | . . . . . +z | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 73) . . . | . . . | . . . 74) . . . | . . . | +z . . . xy . | . [-Z] . | . xz . . xy . | . . . | +z xz . . . . | . . . | . . . . . . | . . . | +z . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . [-Z] . | . . . | +Z . . . . . | . . . | . . . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- +z +z +z | / +Z / | / / / . . . | . . . | / . . . yz . | . . . | . -z . . yz . | . . . | / -z . . . . | . . . | . . . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 75) . . . | . . . | . . . 76) . . / | . . . | . . . . xy . |[-Z] [-Z] [-Z] | . xz . . xy +Z | . . . | . xz . / +Z / | +z +z +z | / / / . . / | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . . [-Z] +z | . . . | . . . . . . | . . . | . . . . [-Z] +z | . . . | . . . . . . | . . . | . . . . [-Z] +z | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . / | . . . | . . . . yz . | . . . | . -z . . yz / | . . . | . -z . . . . | . . . | . . . . . / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 77) . . . | . . . | . . . 78) . . . | . . . | / . . . xy . | . . . | . xz . . xy . | . . . | / xz . . . . | . . . | . . . . . . | . . . | / . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | +z [-Z] . . . . | . . . | . . . . . . | . . . | +z [-Z] . . . . | . . . | . . . . . . | . . . | +z [-Z] . ---------------+---------------+--------------- ---------------+---------------+--------------- / / / | +z +z +z | / +Z / . . . | . . . | / . . . yz . |[-Z] [-Z] [-Z] | . -z . . yz . | . . . | +Z -z . . . . | . . . | . . . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+---------------

R. Jamil

by **rjamil** » Mon Nov 25, 2019 5:52 pm

2 of 3

Code: Select all: XYZ-Transport (55 exemplars) (Row-Column wise): ERI (1 exclusion) 8 10 ---------------+---------------+--------------- ---------------+---------------+--------------- 01) . . . | / +z / | . . . 02) . . . | . . . | . . . . xyz . | +z . +z | . xz . . xyz . | . . . | . xz . . . . | / +z / | . . . . . . | . . . | . . . 03---------------+---------------+---------------03---------------+---------------+--------------- . . . | . . . | . . . / +z / | . . . | . . . . . . | . . . | . . . +z . +z | . . . | . [-Z] . . . . | . . . | . . . / +z / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . [-Z] . | . . . . yz . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 03) . . . | . . . | . . . 04) . . . | . . . | . . . . xyz . | . [-Z] . | . xz . . xyz . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . 03---------------+---------------+---------------03---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | / +z / . . . | . . . | . . . . [-Z] . | . . . | +z . +z . . . | . . . | . . . . . . | . . . | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | / +z / | . . . . . . | . . . | . . . . yz . | +z . +z | . . . . yz . | . . . | . . . . . . | / +z / | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Reduced ERI (up to 2 exclusions) 7 9 ---------------+---------------+--------------- ---------------+---------------+--------------- 05) . [-Z] . | / +Z / | . . . 06) . . . | . . . | . . . . xyz . | +z . +z | . xz . [-Z] xyz . | . . . | . xz . . . . | / / / | . . . . . . | . . . | . . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . / +z / | . . . | . . . . . . | . . . | . . . +Z . / | . . . | . -Z . . . . | . . . | . . . / +z / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . -Z . | . . . . yz . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 09) . . . | / +z / | . . . 10) . . . | . . . | . . . . xyz . | +z . +z | . xz . . xyz . | . [-Z] . | . xz . . . . | / +z / | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . / +z / | / +z / | . . . . [-Z] . | +z . +z | . . . +z . +z | +z . +z | . -Z . . . . | / +z / | . . . / +z / | / +z / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . -Z . | . . . . yz . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 13) . [-Z] . | / +Z / | . . . 14) . . . | . . . | . . . . xyz . | +z . +z | . xz . . xyz [-Z] | . -Z . | . xz . . . . | / / / | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . / +z / | / +z / | . . . . -Z . | +z . +z | . . . / . +Z | +z . +z | . -Z . . . . | / +z / | . . . / +z / | / +z / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . -Z . | . . . . yz . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 17) . . . | / +z / | . . . 18) . . . | . . . | . . . . xyz . | +z . +z | . xz . . xyz . | . -Z . | . xz . . . . | / +z / | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . / +z / | / +Z / | . [-Z] . . -Z . | +Z . / | . . . +z . +z | +z . +z | . -Z . . . . | / +z / | . . . / +z / | / / / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . |[-Z] -Z . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 19) . . . | . . . | . . . 20) . . . | . . . | . . . . xyz . | . -Z [-Z] | . xz . . xyz . | . . . | . xz . . . . | . . . | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . . . . | / / / | / +z / . . . | / . +Z | . (.) . . -Z . | +z . +z | +z . +z . . . | / +z / | . . . . [-Z] . | / +Z / | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | / +z / | . . . . . . | . . . | . . . . yz . | +z . +z | . -z . . yz . | . (.) . | . -z . . . . | / +z / | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Reduced ERI (up to 4 exclusions) ---------------+---------------+--------------- ---------------+---------------+--------------- 21) . [-Z] . | / +Z / | . . . 22) . . . | . . . | . . . . xy . | +z . +z | . xz . . xy [-Z] | . -Z . | . xz . . . . | / / / | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | / +z / | . . . / +z / | / +Z / | . -Z . . -Z . | +Z . / | . . . / . +Z | +z . +z | . -Z . . . . | / +z / | . . . / +z / | / / / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | -Z -Z . | . -z . . yz . | . . . | . -z . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 25) . . . | / +z / | . . . 26) . . . | . . . |[-Z] . . . xyz . | +z . +z | . xz . . xyz . | . . . |[-Z] xz . . . . | / +z / | . . . . . . | . . . |[-Z] . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . / +z / | . . . | +z / / . . . | . . . | . . . +z . +z | . . . | . -Z +z . . . | . . . | . . . / +z / | . . . | +z / / ---------------+---------------+--------------- ---------------+---------------+--------------- [-Z] [-Z] [-Z] | +z . +z | . . . . . . | . . . | . . . . yz . | / -Z / | . . . . yz . | . . . | . . . . . . | / +z / | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Reduced ERI (up to 5 exclusions) ---------------+---------------+--------------- ---------------+---------------+--------------- 29) . [-Z] . | / +Z / | . . . 30) . . . | . . . | -Z . . . xyz . | +z . +z | . xz . . xyz [-Z] | . . . | -Z xz . . . . | / / / | . . . . . . | . . . | -Z . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . / +z / | . . . | +z / / . . . | . . . | . . . / . +Z | . . . | . -Z +z . . . | . . . | . . . / +z / | . . . | +z / / ---------------+---------------+--------------- ---------------+---------------+--------------- -Z -Z -Z | +z . +z | . . . . . . | . . . | . . . . yz . | / -Z / | . -z . . yz . | . . . | . -z . . . . | / +z / | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Line ---------------+---------------+--------------- ---------------+---------------+--------------- 33) . . . | . / . | . . . 34) . . . | . . . | . . . . xyz . | . +Z . | . xz . . xyz . | . [-Z] . | . xz . . . . | . / . | . . . . . . | . . . | . . . 09---------------+---------------+---------------09---------------+---------------+--------------- . . . | . / . | . . . . . . | . . . | . . . . [-Z] . | . +Z . | . . . / +Z / | / +Z / | / / / . . . | . / . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . / . | . . . . . . | . . . | . . . . yz . | . / . | . -z . . yz . | . . . | . -z . . . . | . / . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 37) . . . | . / . | . . . 38) . . . | . . . |[-Z] . . . xyz . | . +Z . | . xz . . xyz . | . . . |[-Z] xz . . . . | . / . | . . . . . . | . . . |[-Z] . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . / . | . . . . . . | . . . | . [-Z] . . . . | . / . | . . . / +Z / | / / / | +Z / / . . . | . / . | . . . . . . | . . . | . [-Z] . ---------------+---------------+--------------- ---------------+---------------+--------------- [-Z] [-Z] [-Z] | . +Z . | . . . . . . | . . . | . . . . yz . |[-Z] / [-Z] | . -z . . yz . | . . . | . -z . . . . | . / . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 39) . . . | . / . | . . . 40) . . . | . . . | . . . . xyz . |[-Z] / [-Z] | . xz . . xyz . | . . . | . xz . . . . | . +Z . | (.) (.) (.) . . . | . . . | . . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . / . | . . . . [-Z] . | . . . | . . . . . . | . / . | . . . / / +Z | / / / | / +Z / . . . | . / . | . . . . [-Z] . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . / . | . . . . . (.) | . . . | . . . . yz . | . +Z . | . -z . . yz (.) | . . . | . -z . . . . | . / . | . . . . . (.) | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Line Ring (multiple exclusions) 13 ---------------+---------------+--------------- ---------------+---------------+--------------- 41) . -YZ . | . . . | . -Z . 42) . -Y . | . / . | . . . -X xy -X | -X -X -X | -X xz -X -XZ xy -XZ |-XZ +Z-X -XZ | -XZ xz -XZ . -YZ . | . . . | . -Z . . -Y . | . / . | . . . 03---------------+---------------+---------------03---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | . / . | . . . / +Z-Y / | / / / | / +Z / . -Y . | . / . | . . . . -YZ . | . . . | . -Z . . -Y . | . / . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | . / . | . . . . yz . | . . . | . (-Z) . -Z yz -Z | -Z +Z -Z | -Z (-Z) -Z . -YZ . | . . . | . -Z . . -Y . | . / . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ERI Ring (multiple exclusions) ---------------+---------------+--------------- ---------------+---------------+--------------- 43) . -YZ . | . . . | . -Z . 44) . -Y . | / +z / | . . . -X xy -X | -X -X -X | -X xz -X -XZ xy -XZ |+z-X -XZ +z-X | -XZ xz -XZ . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . 03---------------+---------------+---------------03---------------+---------------+--------------- / +z-Y / | . . . | / +z / . -Y . | . -Z . | . . . +z -YZ +z | -Z -Z -Z | +z -Z +z . -Y . | . -Z . | . . . / +z-Y / | . . . | / +z / . -Y . | . -Z . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . . yz . | . . . | . (-Z) . -Z yz -Z | +z -Z +z | -Z (-Z) -Z . -YZ . | . . . | . -Z . . -Y . | / +z / | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 45) / +z-Y / | . . . | . . . +z-X xyz +z-X | -XZ -XZ -XZ | -XZ xz -XZ / +z-Y / | . . . | . . . 01---------------+---------------+--------------- . -YZ . | . . . | . . . . -YZ . | . . . | . . . . -YZ . | . . . | . . . ---------------+---------------+--------------- . -YZ . | . . . | . . . . yz . | . . . | . . . . -YZ . | . . . | . . . ---------------+---------------+--------------- ERI ---------------+---------------+--------------- ---------------+---------------+--------------- 49) . . . | . . . | (.) . . 50) . . . | . . . | . . . . xyz . | . . . |[-Z] xz . . xyz . | . . . | . xz . . . . | . . . | (.) . . . . . | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | +z / / (.) [-Z] (.) | . . . | +z . +z . yz . | . . . | . +z +z . yz . | . . . | / +z / . . . | . . . | +z / / . . . | . . . | / +z / ---------------+---------------+--------------- ---------------+---------------+--------------- Box (1 exclusion) 5 6 ---------------+---------------+--------------- ---------------+---------------+--------------- 51) . [-Z] . | +z +z +z | . . . 52) . . . | . . . | . . . . xyz . | +z +z +z | . xz . [-Z] xyz . | . . . | . xz . . . . | / / / | . . . . . . | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . . . . | . . . | . . . +z +z / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | . . . . yz . | . . . | . . . . yz . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- Line (1 exclusion) 1 ---------------+---------------+--------------- ---------------+---------------+--------------- 55) . [-Z] . | . . . | . . . 56) . . +z | . . . | . . . . xyz . | . . . | . xz . [-Z] xyz +z | . . . | . xz . +z +z +z | / / / | +z +z +z . . +z | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . . . . | . . . | . . . . . / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . +z | . . . | . . . . yz . | . . . | . . . . yz +z | . . . | . . . . . . | . . . | . . . . . +z | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 57) . . . | . . . | . . . 58) . . . | . . . | (/) . . . xyz . | . . . | . xz . . xyz . | . . . | +Z xz . . . . | . . . | . . . . . . | . . . | (/) . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- (/) +Z (/) | / / / | +z +z +z . . . | . . . | +z . . . yz . | . . . | . (-Z) . . yz . | . . . | +z (-Z) [-Z] . . . | . . . | . [-Z] . . . . | . . . | +z . . ---------------+---------------+--------------- ---------------+---------------+--------------- Reduced Line Ring (multiple exclusions) 15 ---------------+---------------+--------------- ---------------+---------------+--------------- 59) . -YZ . | . . . | -Z -Z -Z 60) . -Y / | . . . | . . . -X xyz -X | -X -X -X |-XZ xz -XZ -XZ xyz +Z-X | -XZ -XZ -XZ |-XZ xz -XZ / +Z-Y / | / / / | +z +z +z . -Y / | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . -YZ . | . . . | . . . . -Y / | . . . | . . . . -YZ . | . . . | . . . . -Y / | . . . | . . . . -YZ . | . . . | . . . . -Y / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . . . -Z -YZ +z | . . . | . . . . yz . | . . . | . . . -Z yz +z | . . . | . . . . -YZ . | . . . | . . . -Z -YZ +z | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- 15 ---------------+---------------+--------------- ---------------+---------------+--------------- 61) . -Y . | . . . | . -Z . 62) . -Y . | . . . | +z (.) (.) -X xyz -X | -X -X -X | -X xz -X -X xyz -X | -X -X -X |+z-X xz -X . -Y . | . . . | . -Z . . -Y . | . . . | +z (.) (.) 02---------------+---------------+---------------02---------------+---------------+--------------- . -Y . | . . . | . -Z . . -Y . | . . . | / . . . -Y . | . . . | . -Z . . -Y . | . . . | / . . . -Y . | . . . | . -Z . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- +z +z-Y +z | / / / | / +Z / . -Y . | . . . | / . . (.) yz (.) | . . . | . (-Z) . -Z yz -Z | -Z -Z -Z | +Z (-Z) -Z (.) -YZ (.) | . . . | . -Z . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 63) . -YZ . | . . . | -Z -Z -Z 64) . -Y / | . . . | . . . -X xyz -X | -X -X -X | -XZ xz -XZ -XZ xyz +Z-X | -XZ -XZ -XZ | -XZ xz -XZ / +Z-Y / | / / / | / +Z / . -Y / | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y / | . . . | . . . . -YZ . | . . . | . -Z . . -Y / | . . . | . . . . -YZ . | . . . | . -Z . . -Y / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . -YZ . | . . . | . -Z . -Z -YZ / | . . . | . . . . yz . | . . . | . (-Z) . -Z yz +Z | -Z -Z -Z | -Z (-Z) -Z . -YZ . | . . . | . -Z . -Z -YZ / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 65) . -YZ . | . . . | . -Z . 66) . -Y . | . . . | / (.) (.) -X xyz -X | -X -X -X | -X xz -X -XZ xyz -XZ | -XZ -XZ -XZ |+Z-X xz -XZ . -YZ . | . . . | . -Z . . -Y . | . . . | / (.) (.) 02---------------+---------------+---------------02---------------+---------------+--------------- . -YZ . | . . . | . -Z . . -Y . | . . . | / . . . -YZ . | . . . | . -Z . . -Y . | . . . | / . . . -YZ . | . . . | . -Z . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- / +Z-Y / | / / / | / +Z / . -Y . | . . . | / . . (.) yz (.) | . . . | . (-Z) . -Z yz -Z | -Z -Z -Z | +Z (-Z) -Z (.) -YZ (.) | . . . | . -Z . . -Y . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 69) . . . | . . . | (.) . . 70) . . . | . . . | +z . . . xyz . | . . . |[-Z] xz . . xyz . | . . . | +z xz . . . . | . . . | (.) . . . . . | . . . | +z . . 04---------------+---------------+---------------04---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- +z +z +z | / / / | +Z / / (.) [-Z] (.) | . . . | +Z . . . yz . | . . . | . . . . yz . | . . . | / . (.) . . . | . . . | . (.) . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 69a). . . | . . . |[-Z] . . 70a). . . | . . . | (/) . . / . xyz . | . . . | -Z xz . / . xyz . | . . . | +Z xz . . . . | . . . |[-Z] . . . . . | . . . | (/) . . 04---------------+---------------+---------------04---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- (/) +Z (/) | / / / | +Z / / [-Z] -Z [-Z] | . . . | +Z . . . yz . | . . . | . -Z . . yz . | . . . | / -Z -Z . . . | . . . | . -Z . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 73) . . . | . . . | . . . 74) . . . | . . . | +z . . . xyz . | . [-Z] . | . xz . . xyz . | . . . | +z xz . . . . | . . . | . . . . . . | . . . | +z . . 06---------------+---------------+---------------06---------------+---------------+--------------- . . . | . . . | . . . . . . | . . . | / . . . . . | . . . | . . . . [-Z] . | . . . | +Z . . . . . | . . . | . . . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- +z +z +z | / +Z / | / / / . . . | . . . | / . . . yz . | . . . | . -z . . yz . | . . . | / -z . . . . | . . . | . . . . . . | . . . | / . . ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- ---------------+---------------+--------------- 75) . . . | . . . | . . . 76) . . / | . . . | . . . . xyz . |[-Z] [-Z] [-Z] | . xz . . xyz +Z | . . . | . xz . / +Z / | +z +z +z | / / / . . / | . . . | . . . 02---------------+---------------+---------------02---------------+---------------+--------------- . . . | . . . | . . . . [-Z] +z | . . . | . . . . . . | . . . | . . . . [-Z] +z | . . . | . . . . . . | . . . | . . . . [-Z] +z | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+--------------- . . . | . . . | . . . . . / | . . . | . . . . yz . | . . . | . -z . . yz / | . . . | . -z . . . . | . . . | . . . . . / | . . . | . . . ---------------+---------------+--------------- ---------------+---------------+---------------

R. Jamil

by **rjamil** » Mon Nov 25, 2019 5:57 pm

3 of 3

Code: Select all: XY-Wing Type 2 (1 exemplar, up to 5 exclusions) (Box-Line wise): --------------+-------------+----------- -Z XY -Z | . XZ . | . . . . . . | . . . | . . . . . YZ | -Z -Z -Z | . . . 36--------------+-------------+----------- XY-Wing Type 2 Transport (25 examplars) (09-25 YT done) *Line (Useless) Box (Useless) --------------+-------------+----------- --------------+-------------+----------- 01)-z xy -z | . xz . | . . . 02)-z xy -z | . xz . | +z +z +z -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | +z +z +z +z +z yz | -z -z -z | / / / . . yz | -z -z -z | / / / 01--------------+-------------+-----------01--------------+-------------+----------- *Line (Useless) Box (Useless) --------------+-------------+----------- --------------+-------------+----------- 03)-z xy -z | +z xz +z | / / / 04)-z xy -z | . xz . | / / / . . . | -Z -Z -Z | . . . . . . | -Z -Z -Z | +z +z +z . . yz | -z -z -z | . . . . . yz | -z -z -z | +z +z +z 01--------------+-------------+----------- --------------+-------------+----------- *Line (Useless) Box (Useless) --------------+-------------+----------- --------------+-------------+----------- 05)-z xy -z | . xz . | . . . 06)-z xy -z | . xz . | . . . / / / | +z +z +z | +z +z +z / / / | . . . | . . . . . yz | -z -z -z | -Z -Z -Z +z +z yz | -z -z -z | -Z -Z -Z 01--------------+-------------+-----------01--------------+-------------+----------- *Line (Useless) Box (Useless) --------------+-------------+----------- --------------+-------------+----------- 07)-z xy -z | . xz . | -Z -Z -Z 08)-z xy -z | +z xz +z | -Z -Z -Z +z +z +z | / / / | +z +z +z . . . | / / / | . . . . . yz | -z -z -z | . . . . . yz | -z -z -z | . . . 01--------------+-------------+-----------01--------------+-------------+----------- Line Ring Box Ring --------------+-------------+----------- --------------+-------------+----------- 09)-XYz xy -XYz | -XZ xz -XZ | -X -X -X 10)-XYz xy -XYz | -XZ xz -XZ |+z-X +z-X +z-X +z-Y +z-Y +z-Y| +z +z +z | / / / -Y -Y -Y | . . . | / / / -YZ -YZ yz | -z -z -z | . . . -YZ -YZ yz | -z -z -z | +z +z +z 01--------------+-------------+-----------01--------------+-------------+----------- Reduced Line Ring --------------+-------------+----------- --------------+-------------+----------- 11)-XYz xy -XYz | -XZ xz -XZ | -X -X -X 12)-XYz xy -XYz | -XZ xz -XZ | -X -X -X /-Y /-Y +Z-Y | +z +z +z | / / / +z-Y +z-Y +z-Y| / +Z / | / / / -YZ -YZ yz | -z -z -z | . . . -YZ -YZ yz | -z -z -z | . . . 01--------------+-------------+-----------01--------------+-------------+----------- . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- --------------+-------------+----------- 13)-XYz xy -XYz | -XZ xz -XZ | -X -X -X /-Y /-Y +Z-Y | / +Z / | / / / -YZ -YZ yz | -z -z -z | . . . 01--------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- Line Ring ERI Ring --------------+-------------+----------- --------------+-------------+----------- 14)-XYz xy -XYz | -X xz -X | -X -X -X 15)-XYz xy -XYz | -X xz -X | -X -X -X -Y -Y -YZ | . -Z . | . . . -Y -Y -YZ | . -Z . | . . . -Y -Y yz | -z -z -z | . . . -Y -Y yz | -z -z -z | . . . 06--------------+-------------+-----------06--------------+-------------+----------- . . -Z | . -Z . | . . . / / +z | / +z / | . . . / / +Z | / +Z / | / / / +z +z -Z | +z -Z +z | -Z -Z -Z . . -Z | . -Z . | . . . / / +z | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 16)-z xy -z | . xz . | . -Z . 17)-z xy -z | . xz . | . -Z . . . . | . . . | . . . . . . | . . . | . . . . . yz | -z -z -z | . . . . . yz | -z -z -z | . . . 18--------------+-------------+-----------18--------------+-------------+----------- . . . | . . . | . . . / / +z | . . . | / +z / / / +Z | / / / | / +Z / +z +z . | . -Z . | +z . +z . . . | . . . | . . . / / +z | . . . | / +z / --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 18)-z xy -z | . xz . | . . . 19)-z xy -z | . xz . | . . . . . . | . . . | . . . . . . | . . . | . . . . . yz | -z -z -z | . -Z . . . yz | -z -z -z | . -Z . 18--------------+-------------+-----------18--------------+-------------+----------- . . . | . . . | . . . . . . | / +z / | / +z / / / / | / +Z / | / +Z / . . -Z | +z . +z | +z . +z . . . | . . . | . . . . . . | / +z / | / +z / --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 20)-z xy -z | . xz -Z | . . . 21)-z xy -z | . xz -Z | . . . . . . | . . -Z | . . . . . . | . . -Z | . . . . . yz | -z -z -z | . . . . . yz | -z -z -z | . . . 12--------------+-------------+-----------12--------------+-------------+----------- . . . | . -Z . | . . . / / +z | / / +z | . . . / / +Z | / / +Z | / / / +z +z . | +z -Z . | . . . . . . | . -Z . | . . . / / +z | / / +z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 22)-z xy -z | . xz . | . . . 23)-z xy -z | . xz . | . . . . -Z . | . . . | . . . . -Z . | . . . | . . . . -Z yz | -z -z -z | . . . . -Z yz | -z -z -z | . . . 12--------------+-------------+-----------12--------------+-------------+----------- . . -Z | . . . | . . . / +z / | / +z / | . . . / +Z / | / +Z / | / / / +z . -Z | +z . +z | . . . . . -Z | . . . | . . . / +z / | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- ERI --------------+-------------+----------- --------------+-------------+----------- 24)-z xy -z | . xz . | . . . 25)-z xy -z | . xz . | . . . . . . | . . . | . . . . . . | . . . | . . . . . yz | -z -z -z | . . . . . yz | -z -z -z | . . . 06--------------+-------------+-----------06--------------+-------------+----------- / / +z | . . . | . . . . . . | / +z / | . . . +z +z . | . -Z . | . . . . . -Z | +z . +z | . . . / / +z | . . . | . . . . . . | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- XYZ-Wing Transport (30 exemplars) (Box-Line wise): Line 01 Box 02 --------------+-------------+----------- --------------+-------------+----------- 01)-z xyz -z | . xz . | . . . 02)-z xyz -z | . xz . | +z +z +z -Z -Z -Z | . . . | . . . -Z -Z -Z | . . . | +z +z +z +z +z yz | +z +z +z | / / / . . yz | . . . | / / / 01--------------+-------------+-----------01--------------+-------------+----------- Line 07 Box 08 --------------+-------------+----------- --------------+-------------+----------- 03)-z xyz -z | . xz . | -Z -Z -Z 04)-z xyz -z | +z xz +z | -Z -Z -Z +z +z +z | / / / | +z +z +z . . . | / / / | . . . . . yz | . . . | . . . . . yz | +z +z +z | . . . 01--------------+-------------+-----------01--------------+-------------+----------- Line Ring 09 Box Ring 10 --------------+-------------+----------- --------------+-------------+----------- 05)-XYz xyz -XYz| -XZ xz -XZ | -X -X -X 06)-XYz xyz -XYz| -XZ xz -XZ |+z-X +z-X +z-X +z-Y +z-Y +z-Y| +z +z +z | / / / -Y -Y -Y | . . . | / / / -YZ -YZ yz |(-Z)(-Z)(-Z) | . . . -YZ -YZ yz |(-Z)(-Z)(-Z) | +z +z +z 01--------------+-------------+-----------01--------------+-------------+----------- Reduced Line Ring 11 12 --------------+-------------+----------- --------------+-------------+----------- 07)-XYz -XYz xyz| -XZ xz -XZ | -X -X -X 08)-XYz xyz -XYz| -XZ xz -XZ | -X -X -X /-Y /-Y +Z-Y| +z +z +z | / / / +z-Y +z-Y +z-Y| / +Z / | / / / -YZ -YZ yz |(-Z)(-Z)(-Z) | . . . -YZ -YZ yz |(-Z)(-Z)(-Z) | . . . 01--------------+-------------+-----------01--------------+-------------+----------- . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . . . -Z | . . . | . . . . . . | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- 13 --------------+-------------+----------- 09)-XYz -XYz xyz| -XZ xz -XZ | -X -X -X /-Y /-Y +Z-Y| / +Z / | / / / -YZ -YZ yz |(-Z)(-Z)(-Z) | . . . 01--------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- Line Ring 14 ERI Ring 15 --------------+-------------+----------- --------------+-------------+----------- 10)-XYz xyz -XYz| -X xz -X | -X -X -X 11)-XYz xyz -XYz| -XZ xz -XZ | -X -X -X -Y -Y -YZ | . . . | . . . -Y -Y -YZ | . . . | . . . -Y -Y yz | . . . | . . . -Y -Y yz | . . . | . . . 06--------------+-------------+-----------01--------------+-------------+----------- . . . | . . . | . . . / / +z | / +z / | . . . / / +Z | / +Z / | / / / +z +z . | +z . +z | . . . . . . | . . . | . . . / / +z | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line Ring 14 ERI Ring 15 --------------+-------------+----------- --------------+-------------+----------- 12)-XYz -XYz xyz| -X xz -X | -X -X -X 13)-XYz -XYz xyz| -XZ xz -XZ | -X -X -X -Y -Y -YZ | . -Z . | . . . -Y -Y -YZ | . -Z . | . . . -Y -Y yz | . (-Z) . | . . . -Y -Y yz | . (-Z) . | . . . 06--------------+-------------+-----------06--------------+-------------+----------- . . -Z | . -Z . | . . . / / +z | / +z / | . . . / / +Z | / +Z / | / / / +z +z -Z | +z -Z +z | -Z -Z -Z . . -Z | . -Z . | . . . / / +z | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . . . -Z | . -Z . | . . . --------------+-------------+----------- --------------+-------------+----------- Line 16 --------------+-------------+----------- 14)-z xyz -z | . xz . | . -Z . . . . | . . . | . . . . . yz | . . . | . . . 18--------------+-------------+----------- . . . | . . . | . . . / / +Z | / / / | / +Z / . . . | . . . | . . . --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- ERI 17 ERI 17 --------------+-------------+----------- --------------+-------------+----------- 15)-z xyz -z | . xz . | . -Z . 16)-z -z xyz | . xz . | . -Z . . . . | . . . | . . . . . . | . . . | . . . . . yz | . . . | . . . . . yz | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- / / +z | . . . | / +z / / / +z | . . . | / +z / +z +z . | . . . | +z . +z +z +z . | . -Z . | +z . +z / / +z | . . . | / +z / / / +z | . . . | / +z / --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line ERI --------------+-------------+----------- --------------+-------------+----------- 17)-z xyz -z | . xz . | . . . 18)-z xyz -z | . xz . | . . . . . . | . . . | . . . . . . | . . . | . . . . . yz | . . -Z | . . . . . yz | . . -Z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . / +z / | / / +z | . . . / +Z / | / / +Z | / / / +z . +z | +z +z . | . . . . . . | . . . | . . . / +z / | / / +z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line 20 ERI 21 --------------+-------------+----------- --------------+-------------+----------- 19)-z xyz -z | . xz -Z | . . . 20)-z xyz -z | . xz -Z | . . . . . . | . . . | . . . . . . | . . . | . . . . . yz | . . . | . . . . . yz | . . . | . . . 12--------------+-------------+-----------12--------------+-------------+----------- . . . | . . . | . . . / / +z | / / +z | . . . / / +Z | / / +Z | / / / +z +z . | +z +z . | . . . . . . | . . . | . . . / / +z | / / +z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line 20 ERI 21 --------------+-------------+----------- --------------+-------------+----------- 21)-z -z xyz | . xz -Z | . . . 22)-z -z xyz | . xz -Z | . . . . . . | . . -Z | . . . . . . | . . -Z | . . . . . yz | . . (-Z) | . . . . . yz | . . (-Z) | . . . 12--------------+-------------+-----------12--------------+-------------+----------- . . . | . -Z . | . . . / / +z | / / +z | . . . / / +Z | / / +Z | / / / +z +z . | +z -Z . | . . . . . . | . -Z . | . . . / / +z | / / +z | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line 22 ERI 23 --------------+-------------+----------- --------------+-------------+----------- 23)xyz -z -z | . xz . | . . . 24)xyz -z -z | . xz . | . . . . -Z . | . . . | . . . . -Z . | . . . | . . . . -Z yz | . . . | . . . . -Z yz | . . . | . . . 12--------------+-------------+-----------12--------------+-------------+----------- . . . | . . . | . . . / +z / | / +z / | . . . / +Z / | / +Z / | / / / +z . +z | +z . +z | . . . . . . | . . . | . . . / +z / | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line 22 ERI 23 --------------+-------------+----------- --------------+-------------+----------- 25)-z xyz -z | . xz . | . . . 26)-z xyz -z | . xz . | . . . . -Z . | . . . | . . . . -Z . | . . . | . . . . -Z yz | . (-Z) . | . . . . -Z yz | . (-Z) . | . . . 24--------------+-------------+-----------24--------------+-------------+----------- . . . | . . . | . . . / +z / | / +z / | . . . / +Z / | / +Z / | / / / +z . +z | +z . +z | . . . . . . | . . . | . . . / +z / | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- Line 22 ERI 23 --------------+-------------+----------- --------------+-------------+----------- 27)-z -z xyz | . xz . | . . . 28)-z -z xyz | . xz . | . . . . -Z . | . . . | . . . . -Z . | . . . | . . . . -Z yz | . . . | . . . . -Z yz | . . . | . . . 12--------------+-------------+-----------12--------------+-------------+----------- . . -Z | . . . | . . . / +z / | / +z / | . . . / +Z / | / +Z / | / / / +z . -Z | +z . +z | . . . . . -Z | . . . | . . . / +z / | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+----------- ERI 24 25 --------------+-------------+----------- --------------+-------------+----------- 29)-z -z xyz | . xz . | . . . 30)-z -z xyz | . xz . | . . . . . . | . . . | . . . . . . | . . . | . . . . . yz | . . . | . . . . . yz | . . . | . . . 12--------------+-------------+-----------12--------------+-------------+----------- / / +z | . . . | . . . . . . | / +z / | . . . +z +z . | . -Z . | . . . . . -Z | +z . +z | . . . / / +z | . . . | . . . . . . | / +z / | . . . --------------+-------------+----------- --------------+-------------+----------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------------+-------------+----------- --------------+-------------+-----------

R. Jamil

The New Sudoku Players' Forum

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Irregular (W)XYZ-Wings

Re: Irregular (W)XYZ-Wings

Irregular vs Hybrid vs Transport Wings

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