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.
Any polytope that is uniform, scaliform, CRF or isogonal will preserve these attributes in its prism. In addition, the prism of any orbiform polytope is a segmentotope.
The vertex figure of a prism is generally a pyramid of the vertex figure of the base. For example, the icosahedral prism has a pentagonal pyramid-shaped vertex figure.
If the base polytope has circumradius r and the height of the prism is h, the circumradius of the prism is given simply by √r2+(h/2)2, and its hypervolume is equal to vh where v is the hypervolume of the base.
If the prism's base is also a prism, then it can also be seen as a duoprism of a rectangle and the base of the base facet.
External links[edit | edit source]
- Klitzing, Richard. "n/d-p".