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Midpoint augmentation, a term introduced here, is a variant of conventional augmentation in which each facial polygon is replaced by a triangular polygon joining vertices ...

The Archimedean duals are the 13 duals of the 13 Archimedean solids, sometimes called the Catalan solids. They are summarized in the following table and illustrated below ...

Bilinski (1960) noted that by collapsing any one of the five zones of the rhombic icosahedron, a second rhombic dodecahedron distinct from the dual polyhedron of the ...

The dual polyhedra of the Archimedean solids, given in the following table. They are known as Catalan solids in honor of the Belgian mathematician who first published them in ...

The great rhombicuboctahedral graph is the cubic Archimedean graph on 48 nodes and 72 edges that is the skeleton of the great rhombicuboctahedron as well as the great ...

The snub cube, also called the cubus simus (Kepler 1619, Weissbach and Martini 2002) or snub cuboctahedron, is an Archimedean solid having 38 faces (32 triangular and 6 ...

The quasirhombicuboctahedron is the name given by Wenninger (1989, p. 132) to the uniform polyhedron with Maeder index 17 (Maeder 1997), Wenninger index 85 (Wenninger 1989), ...

Stellation is the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect (Wenninger 1989). The ...

There are a number of attractive polyhedron compounds consisting of five octahedra. The first octahedron 5-compound is a polyhedron compound composed of five octahedra ...

The 13 Archimedean solids are the convex polyhedra that have a similar arrangement of nonintersecting regular convex polygons of two or more different types arranged in the ...