A prism is a polytope formed as the prism product of a given polytope (the base) and a dyad. It can be thought of as the base extruded into the next dimension. Prisms can be constructed in any dimension. The dual of a prism is the bipyramid of the base's dual.
The facets of a prism are 2 copies of the base polytope plus prisms of whatever facets the base has. For example, a truncated icosahedral prism has as cells 2 truncated icosahedra (the bases), 12 pentagonal prisms (from the pentagons), and 20 hexagonal prisms (from the hexagons). It generally has double the amount of vertices of the base.
The hypercube of each dimension is the prism of the hypercube of the previous dimension.
If the base polytope has circumradius r and the height of the prism is h, the circumradius of the prism is given simply by √, and its hypervolume is equal to vh where v is the hypervolume of the base.
[edit | edit source]
- Klitzing, Richard. "n/d-p".