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It would be nice to have a definition of "polypon"! - N. J. A. Sloane (njas(AT)research.att.com), May 09 2007
Comments from R. J. Mathar, Dec 10 2007: (Start)
By looking at the Clarke pictures, I guess that the unit element is a triangle with
internal angles of 120 degrees and two of 30 degrees. The polypons are
connected, nonoverlapping assemblies of these, where connectivity is defined
via common sides; a common point is not enough. Only non-congruential
assemblies are counted, those which cannot be mapped onto each other by
rotations, translations or mirrors along a line or point. However, the
polypons are not all of these, because some of the free-form assemblies of
this kind would need placement of the unit that violates the format by the
grid. (The first case where this happens is with assemblies of 3 units: the
picture shows 2 examples with assemblies of 3 units, but I can imagine at
least 1 more where the unit would need to hide/cover one of the grid's edges.) (End)
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