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 "D_3h" 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:

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

See also

*Prism (geometry)
*Semiregular k 21 polytope

External links

*
* [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]