Triangular prism

Uniform Triangular prism
Type	Prismatic uniform polyhedron
Elements	F = 5, E = 9 V = 6 (χ = 2)
Faces by sides	3{4}+2{3}
Schläfli symbol	t{2,3} or {3}x{}
Wythoff symbol	2 3 | 2
Coxeter-Dynkin
Symmetry	D3h
References	U76(a)
Dual	Triangular dipyramid
Properties	convex
Vertex figure 4.4.3

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.

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.

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

The symmetry group of a right 3-sided prism with triangular base is D_3h of order 12. The rotation group is D₃ of order 6.

The symmetry group does not contain inversion.

It can be considered as a truncated trigonal hosohedron.

Volume

The volume of any prism is the product of the area of the base and the distance between the two bases. 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:

Where b is the triangle base length, h is the triangle height, and l is the length.

See also

• Prism (geometry)
• Semiregular k 21 polytope

External links

• Weisstein, Eric W., "Triangular prism" from MathWorld.
• Interactive Polyhedron: Triangular Prism