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The Cairo tessellation is a tessellation appearing in the streets of Cairo and in many Islamic decorations. Its tiles are obtained by projection of a dodecahedron, and it is ...

Let each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces. Call the resulting polyhedron the local cell. Then the local density is ...

The collapsoids are a class of non-convex collapsible polyhedra. They can be constructed by replacing each edge of a dodecahedron or icosahedron by the diagonal of a pyramid ...

The Kepler-Poinsot polyhedra are four regular polyhedra which, unlike the Platonic solids, contain intersecting facial planes. In addition, two of the four Kepler-Poinsot ...

The pentagonal hexecontahedron is the 60-faced dual polyhedron of the snub dodecahedron A_8 (Holden 1971, p. 55). It is Wenninger dual W_(18). A tetrahedron 10-compound, cube ...

The polyhedron compound of the icosahedron (U_(22)) and the great dodecahedron (U_(35)), sometimes known as the small cid. Four faces meet at each edge of the small complex ...

The endodocehedron, also called the concave pyrohedral dodecahedron, is the concave solid corresponding to the interior void formed when each face of a regular dodecahedron ...

An isohedron is a convex polyhedron with symmetries acting transitively on its faces with respect to the center of gravity. Every isohedron has an even number of faces ...

A cube 30-compound can be constructed from the vertices of the first dodecahedron 6-compound. It will be implemented in a future version of the Wolfram Language as ...

A number of attractive 10-compounds of the regular icosahedron can be constructed. The compound illustrated above will be implemented in a future version of the Wolfram ...