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The surface of a deltoidal hexecontahedron has 60 congruent faces. Edge-connected faces are called polykites. Reflections are included separately in the counts. Polykites can have from 1 to 60 faces.

These polykites are counted up to the full icosahedral group (order 120) of the deltoidal hexecontahedron. - Peter Kagey, Apr 28 2025

It would be nice to have a definition of "polypon"! - N. J. A. Sloane, May 09 2007

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.) - R. J. Mathar, Dec 10 2007