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Tuesday, December 15, 2015

Square Triangles

Filed under: General,Geometry — m759 @ 3:57 PM

Click image for some background.

Exercise:  Note that, modulo color-interchange, the set of 15 two-color
patterns above is invariant under the group of six symmetries of the
equilateral triangle. Are there any other such sets of 15 two-color triangular
patterns that are closed as sets , modulo color-interchange, under the six
triangle symmetries and  under the 322,560 permutations of the 16
subtriangles induced by actions of the affine group AGL(4,2)
on the 16 subtriangles' centers , given a suitable coordinatization?

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