Triangular prism
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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 | D_{3h} |
References | U_{76(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.
If the faces are squares, it is a uniform polyhedron.
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 D_{3} of order 6.
The symmetry group does not contain inversion.
Volume
The volume of any right 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 or rectangle 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.