Prism (geometry)

From Wikipedia, the free encyclopedia

For other uses, see Prism (disambiguation).

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.

1 General, right and uniform prisms
2 Uniform prisms
3 Area and volume
4 Symmetry
5 Star prisms
6 External links

[edit] 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 if 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.

An n-prism, made of regular polygons ends and rectangle sides approaches a cylindrical solid as n approaches infinity.

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.

[edit] 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

[edit] 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).

[edit] 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.