Uniform hexagonal prism
Type	Prismatic uniform polyhedron
Elements	F = 8, E = 18, V = 12 (χ = 2)
Faces by sides	6{4}+2{6}
Schläfli symbol	t{2,6} or {6}×{}
Wythoff symbol	2 6 | 2 2 2 3 |
Coxeter diagrams
Symmetry	D6h, [6,2], (*622), order 24
Rotation group	D6, [6,2]+, (622), order 12
References	U76(d)
Dual	Hexagonal dipyramid
Properties	convex, zonohedron
Vertex figure 4.4.6

In geometry, the hexagonal prism is a prism with hexagonal base. The shape has 8 faces, 18 edges, and 12 vertices.

Since it has eight 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 the dissimilarity of the various eight-sided figures, the term is rarely used without clarification.

As a semiregular (or uniform) polyhedron

If faces are all regular, the hexagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the fourth in an infinite set of prisms formed by square sides and two regular polygon caps. It can be seen as a truncated hexagonal hosohedron, represented by Schläfli symbol t{2,6}. Alternately it can be seen as the Cartesian product of a regular hexagon and a line segment, and represented by the product {6}x{}. The dual of a hexagonal prism is a hexagonal bipyramid.

The symmetry group of a right pentagonal prism is D_6h of order 24. The rotation group is D₆ of order 12.

Volume

As in most prisms, the volume is found by taking the area of the base, with a side length of ${\displaystyle a}$, and multiplying it by the height ${\displaystyle h}$.

${\displaystyle V={\frac {3{\sqrt {3))}{2))a^{2}\times h}$

Other images

A translucent model

Use

It is an element of four prismatic uniform honeycombs:

Hexagonal prismatic honeycomb

Triangular-hexagonal prismatic honeycomb

Snub triangular-hexagonal prismatic honeycomb

Rhombitriangular-hexagonal prismatic honeycomb

It is also an element of many four-dimensional uniform polychora, including: the truncated octahedral prism, omnitruncated 5-cell runcitruncated 5-cell, omnitruncated tesseract, runcitruncated 16-cell, runcitruncated 24-cell, omnitruncated 24-cell, omnitruncated 120-cell, runcitruncated 600-cell.