PRISM (GEOMETRY)

{| border="1" bgcolor="#ffffff" cellpadding="5" align="right" style="margin-left:10px" width="250"
!bgcolor=#e7dcc3 colspan=2|Set of uniform prisms
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|align=center colspan=2|
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|bgcolor=#e7dcc3|Type||uniform polyhedron
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|bgcolor=#e7dcc3|Faces||2 p-gons, p squares
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|bgcolor=#e7dcc3|Edges||3p
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|bgcolor=#e7dcc3|Vertices||2p
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|bgcolor=#e7dcc3|Schläfli symbol||t{2,p}
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|bgcolor=#e7dcc3|Coxeter-Dynkin diagram||
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|bgcolor=#e7dcc3|Vertex configuration||4.4.p
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|bgcolor=#e7dcc3|Symmetry group||''D''_''ph''
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|bgcolor=#e7dcc3|Dual polyhedron||bipyramids
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|bgcolor=#e7dcc3|Properties||convex, semi-regular vertex-transitive
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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.

Contents

General, right and uniform prisms

Area and volume

Symmetry

See also

External links

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 right 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'.
An equilateral square prism is simply a cube.

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, or the height (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 4''n'', 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 2''n'', 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 ''D_nh'' contains inversion iff ''n'' is even.

See also

★ Prismatic uniform polyhedron.

★ Cylinder (geometry)

External links

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★

★ Nonconvex Prisms and Antiprisms

★ Surface Area MATHguide

★ Volume MATHguide

★ Paper models of prisms and antiprisms Free nets of prisms and antiprisms

★ Paper models of prisms and antiprisms