pentahedron

In geometry, a pentahedron (plural: pentahedra) is a polyhedron with five faces. Since there are no face-transitive polyhedra with five sides and there are two distinct topological types, this term is rarely used.

With regular polygon faces, the two topological forms types are the square pyramid and triangular prism. Geometric variations with irregular faces can also be constructed.

Name	Picture	Vertices	Edges	Faces	Faces by type
Square pyramid (Pyramid family)		5	8	5	4 triangles 1 square
Triangular prism (Prism family)		6	9	5	2 triangles 3 squares

The square pyramid can be seen as a degenerate triangular prism where one edge of its side edges is collapsed into a point, losing one edge and one vertex, and changing two squares into triangles.

Hosohedron

There is a third topological polyhedral figure with 5 faces, degenerate as a polyhedron, it exists as a spherical tiling of digon faces, called a pentagonal hosohedron with Schläfli symbol {2,5}. It has 2 (antipodal point) vertices, 5 edges, and 5 digonal faces.

External links

• Weisstein, Eric W., "Pentahedron" from MathWorld.

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