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The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" ...

A triacontahedron is a 30-faced polyhedron. Examples include the 14-gonal antiprism, biaugmented truncated cube (Johnson solid J_(67)), 15-gonal dipyramid, 28-gonal prism, ...

An elongated square pyramid is a solid formed by attaching a square pyramid atop a square prism. Such a solid might also be termed an obelisk (although that term is also used ...

A hexagon tiling is a tiling of the plane by identical hexagons. The regular hexagon forms a regular tessellation, also called a hexagonal grid, illustrated above. There are ...

The cubical graph is the Platonic graph corresponding to the connectivity of the cube. It is isomorphic to the generalized Petersen graph GP(4,1), bipartite Kneser graph ...

A polyhedron or plane tessellation is called semiregular if its faces are all regular polygons and its corners are alike (Walsh 1972; Coxeter 1973, pp. 4 and 58; Holden 1991, ...

A cubic polyhedral graph is a graph that is both cubic and polyhedral. The numbers of cubical polyhedral graphs on n=2, 4, ... nodes are 0, 1, 1, 2, 5, 14, 50, 233, 1249, ... ...

In three dimensions, a parallelepiped is a prism whose faces are all parallelograms. Let A, B, and C be the basis vectors defining a three-dimensional parallelepiped. Then ...

A benzenoid is a fusene that is a subgraph of the regular hexagonal lattice (i.e., a simply connected polyhex). The numbers of n-hexagon benzenoids for n=1, 2, ... are 1, 1, ...

A Möbius ladder, sometimes called a Möbius wheel (Jakobson and Rivin 1999), of order n is a simple graph obtained by introducing a twist in a prism graph of order n that is ...