# Hexagonal prism

In geometry, the hexagonal prism is a prism with hexagonal base. This polyhedron has 8 faces, 18 edges, and 12 vertices.[1]

Since it has 8 faces, it is an octahedron. However, the term octahedron is primarily used to refer to the regular octahedron, which has eight triangular faces. Because of the ambiguity of the term octahedron and tilarity of the various eight-sided figures, the term is rarely used without clarification.

Before sharpening, many pencils take the shape of a long hexagonal prism.[2]

The symmetry group of a right hexagonal prism is D6h of order 24. The rotation group is D6 of order 12.

The topology of a uniform hexagonal prism can have geometric variations of lower symmetry, including:

It exists as cells of four prismatic uniform convex honeycombs in 3 dimensions:

It also exists as cells of a number of four-dimensional uniform 4-polytopes, including:

This polyhedron can be considered a member of a sequence of uniform patterns with vertex figure (4.6.2p) and Coxeter-Dynkin diagram . For p < 6, the members of the sequence are omnitruncated polyhedra (zonohedrons), shown below as spherical tilings. For p > 6, they are tilings of the hyperbolic plane, starting with the truncated triheptagonal tiling.