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Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...

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 geodesic dome is a triangulation of a Platonic solid or other polyhedron to produce a close approximation to a sphere (or hemisphere). The nth order geodesation operation ...

The cubitruncated cuboctahedron (called the cubotruncated cuboctahedron by Wenninger 1971, p. 121) is the uniform polyhedron with Maeder index 16 (Maeder 1997), Wenninger ...

The disdyakis dodecahedron is the dual polyhedron of the Archimedean great rhombicuboctahedron A_3 and Wenninger dual W_(15). It is also called the hexakis octahedron ...

A hexahedral graph is a polyhedral graph on six vertices. There are seven distinct hexahedral graphs (illustrated above) which, through duality, correspond to seven convex ...

A parallelohedron is a space-filling polyhedron that fills space using an infinite number of similarly situated copies (Tutton 1964, pp. 567 and 723; Coxeter 1973, pp. ...

The supersphere is the algebraic surface that is the special case of the superellipse with a=b=c. It has equation |x/a|^n+|y/a|^n+|z/a|^n=1 (1) or |x|^n+|y|^n+|z|^n=a^n (2) ...

The Archimedean duals in general have many stellations. The following table extracted from Webb gives a partial enumeration. In the table, E denotes counts of enantiomorphous ...

Barnette's conjecture asserts that every 3-connected bipartite cubic planar graph is Hamiltonian. The only graph on nine or fewer vertices satisfying Barnette's conditions is ...