[Update 3]

Link to udosuks collection of deciphered sample grids.

Link to a summary of symmetrical solution techniques.

[Added:] Link to Red Ed's list of all 122 symmetries (also combined, now with generating sets in sample grids).

The columns have the following meaning:

Name

M..representative mapping for the symmetry

C..class number in Red Ed's class table

N..number of invariant sudoku grids with this symmetry, given by Red Ed

L..Length of the (longest) cell cycles of this symmetry

F..number of fixed cells

S..special techniques for solving puzzles with this symmetry known: Y..yes, N..no, U..Unnecessary

Comment

- Code: Select all
`M C N L F S`

1. Fixed boxes

Mini-Rows (MR) C 8 107.495.424 3 0 N equivalent to Mini-Columns (MC)

2 MR, 1 MD CR1 7 21.233.664 3 0 Y

1 MR, 2 MD CR1R2 9 4.204.224 3 0 Y

Mini-Diagonals(MD) CR 10 2.508.084 3 0 Y

2. Boxes move in bands

Jumping-Rows (JR) S 25 14.837.760 3 0 N

2 JR, 1 GR SR1 28 2.085.120 3 0 Y

1 JR, 2 GR SR1R2 30 294.912 3 0 Y

Gliding-Rows (GR) SR 32 6.342.480 3 0 Y

Full-Rows (FR) SC1 27 5.184 9 0 U

2 FR, 1 WR SR1C1 26 2.592 9 0 U

1 FR, 2 WR SR1R2C1 29 1.296 9 0 U

Waving-Rows (WR) SRC1 31 648 9 0 U

3. Boxes move triangular (B 159, 267, 368)

Jumping-Diagonals (JD) BS 22 323.928 3 0 Y also "Block symmetry"

Broken-Columns (BC) BSR1 24 288 9 0 U

Full-Diagonals(FD) BSR1C1 23 162 9 0 U

4. Rotational symmetries

Half-Turn (HT) DD2 79 155.492.352 2 1 Y also "180° rotational symmetry"

Quarter-Turn (QT) DBxRx 86 13.056 4 1 Y also "90° rotational symmetry", has HT symmetry too

5. Diagonal symmetries

Diagonal-Mirror (DM) D 37 30.258.432 2 9 Y also "diagonal symmetry"

DM+JD DBS 43 288 6 0 Y

DM+MD DRC 40 1.854 6 0 Y

6. Sticks symmetries

Column-Sticks (CS) BxCx 134 449.445.888 2 9 Y also "sticks symmetry"

CS+MC BxCxR 135 27.648 6 0 U

CS+JR BxCxS 145 13.824 6 0 U

CS+ GR/Band2,JR/B13 BxCxSR2 144 3.456 6 0 U

CS+GR BxCxSR 142 6.480 6 0 U

CS+ JR/B2,GR/B13 BxCxSR1R3 143 1.728 6 0 U

Meaning of the shortcuts of the equivalence operations (to be read from left to right, eg DBS means S after B after D)

B..cyclically move the bands downwards (B123->B231)

S..cyclically move the stacks rightwards (S123->S231)

Bx..exchange B1 and B3 (B123->B321)

Sx..exchange S1 and S3 (S123->S321)

R1 (R2, R3)..cyclically move the rows in band 1(2,3) downwards (r123->r231)

C1 (C2, C3)..cyclically move the columns in stack 1 (2.3) rightwards (c123->c231)

R..cyclically move the rows in all bands downwards (R1R2R3 or r123456789->r231564897)

C..cyclically move the colums in all stacks rightwards (C1C2C3 or r123456789->r231564897)

Rx..invert the order (exchange the first and 3rd) of the rows in all bands (r123456789->r321654987)

Sx..invert the order (exchange the first and 3rd) of the colums in all stacks (c123456789->c321654987)

D..mirror at the main diagonal from r1c1 to r9c9 (r123456789<->c123456789)

D2..mirror at the subdiagonal from r1c9 to r9c1 (r123456789<->c987654321)