Triangular prism

﻿
Triangular prism

In geometry, a triangular prism or three-sided prism is a type of prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

If the sides are squares, it is called a uniform polyhedron. In general the sides can be congruent rectangles.

Equivalently, it is a pentahedron of which two faces are parallel, while the surface normals of the other three are in the same plane (which is not necessarily parallel to the base planes). These three faces are parallelograms. All cross-sections parallel to the base faces are the same triangle.

A right triangular prism is semiregular if the base faces are equilateral triangles, and the other three faces are squares.

A general right triangular prism can have rectangular sides.

The dual of a triangular prism is a 3-sided bipyramid.

The symmetry group of a right 3-sided prism with regular base is "D3h" of order 12. The rotation group is "D3" of order 6.

The symmetry group does not contain inversion.

Volume

The volume of "any" prism is the product of the area of the base and the distance between the two base faces. In this case the base is a triangle so we simply need to compute the area of the triangle and multiply this by the length of the prism:

$V = frac\left\{1\right\}\left\{2\right\} bhl.$Where b is the triangule base length, h is the triangle height, and l is the length.

*Prism (geometry)
*Semiregular k 21 polytope

*
* [http://polyhedra.org/poly/show/22/triangular_prism Interactive Polyhedron: Triangular Prism]
* [http://www.korthalsaltes.com/triangular_prism.htm Paper model triangular prism] Prism nets
* [http://www.lifeisastoryproblem.org/explore/net_triangular_prism.pdf Printable net of a Triangular Prism] [http://www.lifeisastoryproblem.org Life is a Story Problem.org]

Wikimedia Foundation. 2010.

Look at other dictionaries:

• triangular prism — noun A prism with a triangular base …   Wiktionary

• triangular prism — noun a prism whose bases are triangles • Hypernyms: ↑prism …   Useful english dictionary

• triangular prism — triangle shaped transparent body that fractures light rays into the colors of the spectrum …   English contemporary dictionary

• Biaugmented triangular prism — Infobox Polyhedron with net Polyhedron Type=Johnson J49 J50 J51 Face List=3x2+4 triangles 1 square Edge Count=17 Vertex Count=8 Symmetry Group= C 2v Vertex List=2(35) 2(34) 4(33.4) Dual= Property List=convex Net In geometry, the biaugmented… …   Wikipedia

• Augmented triangular prism — Infobox Polyhedron with net Polyhedron Type=Johnson J48 J49 J50 Face List=3x2 triangles 2 squares Edge Count=13 Vertex Count=7 Symmetry Group= C 2v Vertex List=2(3.42) 1(34) 4(33.4) Dual= Property List=convex Net In geometry, the augmented… …   Wikipedia

• Triaugmented triangular prism — Infobox Polyhedron with net Polyhedron Type=Johnson J 50 J51 J52 Face List=2+2x6 triangles Edge Count=21 Vertex Count=9 Symmetry Group= D 3h Vertex List=3(34) 6(35) Dual= Property List=convex, deltahedron Net In geometry, the triaugmented… …   Wikipedia

• Prism — (pr[i^]z m), n. [L. prisma, Gr. pri sma, fr. pri zein, pri ein, to saw: cf. F. prisme.] 1. (Geom.) A solid whose bases or ends are any similar, equal, and parallel plane figures, and whose sides are parallelograms. [1913 Webster] Note: Prisms of… …   The Collaborative International Dictionary of English

• Prism (optics) — For other uses, see Prism (disambiguation). A plastic prism In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional… …   Wikipedia

• prism — /priz euhm/, n. 1. Optics. a transparent solid body, often having triangular bases, used for dispersing light into a spectrum or for reflecting rays of light. 2. Geom. a solid having bases or ends that are parallel, congruent polygons and sides… …   Universalium

• Triangular dipyramid — For the related molecular geometry see trigonal bipyramid molecular geometry Infobox face uniform polyhedron Polyhedron Type=Dipyramid and Johnson J11 J12 J13 Face List=6 triangles Edge Count=9 Vertex Count=5 Symmetry Group= D 3h Face Type=V3.4.4 …   Wikipedia