Zometool (Pentaelongated icosidodecahedron)

Untitled, injection-molded plastic. Contributed by Studio Infinity.

[107 F, 210 E, 105 V] Start with an icosidodecahedron, one of the Archimedean solids. (Its faces are shown in blue in this model). Succesively “stretch” or elongate it in five different directions, interpolating parallelograms (some of which are rectangles) along a belt or “zone” each time it is elongated. That process, called “zonification”, produces this polyhedron. The edges of each zone are colored a single color: two of the zones are red, and three of the zones are white.

The five directions used for these elongations are five of the six axes of fivefold symmetry of the original icosidodecahedron. The “equator” of the resulting oblate polyhedron is shown in black in this model. It could be elongated one more time, perpendicular to this equator (i.e., along the sixth axis of fivefold symmetry) to produce a nearly spherical model, restoring full icosahedral symmetry. (However, the resulting polyhedron would have to be situated almost two feet beyond the end of Polyplane’s superstructure.)