Re: Steven Cullinane is a Crank

On the off chance that "Bob Stewart" is not "crankbuster" under another name, here is a reply:

Your statement that "if each of the permuted objects has some geometrical symmetry, then these resulting permutations will display symmetries too" is false, as you would know if you had tried to find a counterexample... Such as (for instance) the four diffent square patterns obtained by division of a square into black and white halves by horizontal or vertical (rather than diagonal) midlines.

As for affine geometry, see
http://log24.com/theory/geometry.html.

This site contains an explanation, written for those with some mathematical maturity, of the role played by the affine group AGL(4,2) in the geometry of the 4x4 square.

That group, by the way, is where the number 322,560, quoted by the deeply confused "crankbuster," comes from.
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