Pentagonal prism

If faces are all regular, the pentagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the third in an infinite set of prisms formed by square sides and two regular polygon caps. It can be seen as a truncated pentagonal hosohedron, represented by Schläfli symbol t{2,5}. Alternately it can be seen as the Cartesian product of a regular pentagon and a line segment, and represented by the product {5}×{}. The dual of a pentagonal prism is a pentagonal bipyramid. The symmetry group of a right pentagonal prism is D5h of order 20. The rotation group is D5 of order 10. ==Volume==

The volume, as for all prisms, is the product of the area of the pentagonal base times the height or distance along any edge perpendicular to the base. For a uniform pentagonal prism with edges h the formula is :\frac{h^3}{4}\sqrt{5(5 + 2\sqrt{5})} \approx 1.72h^3 == Use ==

Nonuniform pentagonal prisms called pentaprisms are also used in optics to rotate an image through a right angle without changing its chirality. In 4-polytopes It exists as cells of four nonprismatic uniform 4-polytopes in four dimensions: == Related polyhedra ==

: has pentagonal dihedral symmetry and has the same vertices as the uniform pentagonal prism. ==External links ==