Prism (geometry)

Set of uniform prisms
Type	uniform polyhedron
Faces	2 n-gons, n squares
Edges	3n
Vertices	2n
Vertex configuration	4.4.n
Symmetry group	D_nh
Dual polyhedron	bipyramids
Properties	convex, semi-regular vertex-uniform

In geometry, an n-sided prism is a polyhedron made of an n-sided polygonal base, a translated copy, and n faces joining corresponding sides. Thus these joining faces are parallelograms. All cross-sections parallel to the base faces are the same. A prism is a subclass of the prismatoids.

General, right and uniform prisms

A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. This applies iff the joining faces are rectangular.

In the case of a rectangular or square prism there may be ambiguity because some texts may mean a right rectangular-sided prism and a right square-sided prism.

The term uniform prism can be used for a right prism with square sides since such prisms are in the set of uniform polyhedra.

Right prisms with regular bases and equal edge lengths form one of the two infinite series of semiregular polyhedra, the other series being the antiprisms.

The dual of a uniform prism is a bipyramid.

A parallelepiped is a prism of which the base is a parallelogram, or equivalently a polyhedron with 6 faces which are all parallelograms.

A right rectangular prism is also called a cuboid, or informally a rectangular box. A right square prism is simply a square box, and may also be called a square cuboid.

Uniform prisms

4.4.3
4.4.4
4.4.5
4.4.6
4.4.8
4.4.10
4.4.12

...	...	...	4.4.N

Area and volume

The volume of a prism is the product of the area of the base and the distance between the two base faces (in the case of a non-right prism, note that this means the perpendicular distance).

Symmetry

The symmetry group of a right n-sided prism with regular base is D_nh of order 4n, except in the case of a cube, which has the larger symmetry group O_h of order 48, which has three versions of D_4h as subgroups. The rotation group is D_n of order 2n, except in the case of a cube, which has the larger symmetry group O of order 24, which has three versions of D₄ as subgroups.

The symmetry group contains inversion iff n is even.

Star prisms

There are also uniform prisms that can be constructed by star polygons: {n/m} = {5/2}, {7/3}, {7/4}, {8/3}, {9/2}, {9/4}, {10/3}...

{5/2}
{7/2}
{7/3}

External links

Paper models of prisms and antiprisms Free nets of prisms and antiprisms
Paper models of prisms and antiprisms
Prisms (Cross Section Illustration)
The Uniform Polyhedra
http://mathworld.wolfram.com/Prism.html
Virtual Reality Polyhedra The Encyclopedia of Polyhedra
- VRML models (George Hart) <3> <4> <5> <6> <7> <8> <9> <10>