# 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 *D _{6h}* of order 24. The rotation group is

*D*of order 12.

_{6}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.