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A polygon can be defined (as illustrated above) as a geometric object "consisting of a number of points (called vertices) and an equal number of line segments (called sides), ...

An unfolding is the cutting along edges and flattening out of a polyhedron to form a net. Determining how to unfold a polyhedron into a net is tricky. For example, cuts ...

The cocktail party graph of order n, also called the hyperoctahedral graph (Biggs 1993, p. 17), n-octahedron graph O_n (Jungerman and Ringel 1978), matching graph (Arvind et ...

Generally, a face is a component polygon, polyhedron, or polytope. A two-dimensional face thus has vertices and edges, and can be used to make cells. More formally, a face is ...

The term "hyperoctahedron" may refer to the 16-cell polytope in 4 dimensions, or more generally to an n-dimensional cross polytope.

A generalization of a solid such as a cube or a sphere to more than three dimensions. A four-dimensional version of a polyhedron is known as a polytope.

An (n-2)-dimensional face of an n-dimensional polytope.

Any sum of a selection of Pi_ks, where Pi_k denotes a k-D polytope.

The 27 real or imaginary lines which lie on the general cubic surface and the 45 triple tangent planes to the surface. All are related to the 28 bitangents of the general ...

The space |K| which is the subset of R^n that is the union of the simplices in a simplicial complex K. The term polytope is sometimes used as a synonym for underlying space ...