Pentagonal prism

Uniform Pentagonal prism
Type	Prismatic uniform polyhedron
Elements	F = 7, E = 15 V = 10 (χ = 2)
Faces by sides	5{4}+2{5}
Schläfli symbol	t{2,5} or {5}x{}
Wythoff symbol	2 5 | 2
Coxeter-Dynkin
Symmetry	D5h, [5,2], (*55)
References	U76(c)
Dual	Pentagonal dipyramid
Properties	convex
Vertex figure 4.4.5

In geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with 7 faces, 15 edges, and 10 vertices.

As a semiregular (or uniform) polyhedron

If faces are all regular, the pentagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the third in an infinite set of prisms formed by square sides and two regular polygon caps. It can be seen as a truncated pentagonal hosohedron, represented by Schläfli symbol t{2,5}. Alternately it can be seen as the Cartesian product of a regular pentagon and a line segment, and represented by the product {5}x{}. The dual of a pentagonal prism is a pentagonal bipyramid.

The symmetry group of a right pentagonal prism is D_5h of order 20. The rotation group is D₅ of order 10.

Volume

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

See also

• Set of prisms
• Triangular prism
• Cube Square-capped prism
• Hexagonal prism

Use

Nonuniform pentagonal prisms called Pentaprisms are also used in optics to rotate an image through a right angle without changing its chirality.

In polychora

It exists as cells of four polychora in 4 dimensions:

cantellated 600-cell	cantitruncated 600-cell	runcinated 600-cell	runcitruncated 600-cell

External links

• Weisstein, Eric W., "Pentagonal prism" from MathWorld.
• Pentagonal Prism Polyhedron Model -- works in your web browser