I am a newbie here, and just a recent Sudoku addict, but from a programming approach.

Excuse me if what I say is blindingly obvious and known to everyone from first principles.

We depict the grid as 2D, but it seems very obvious that the object is in fact 3D, with our Z dimension represented in flatland as a small square grid.

My first programming instinct had been to think about row, column and square objects separately, but if I view the grid in X,Y,Z terms then the symmetry becomes much more useful at least from a conceptual viewpoint.

So then Row, Column and Square are all totally interchangeable; any rule which involves Row and Column equally applies to Column and Square , Square and Row.

Starting with A1 as the origin (0,0,0) we can mentally rotate and see the grid in conventional 3D form with I9 at (8,8,8)

We can apply transformations of rotation or shift of origin or interchange of XYZ without impact

Is this XYZ approach a useful way of viewing Sudoku?