Pentahedron

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For the Sylvester pentahedron of a cubic surface, see quaternary cubic.

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 less frequently used than tetrahedron or octahedron.

With regular polygon faces, the two topological forms 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)
Square pyramid.png 5 8 5 4 triangles
1 square
Triangular prism
(Prism family)
Triangular prism.png 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.

An irregular pentahedron can be a non-convex solid.

Hosohedron[edit]

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[edit]