What Shape Has 5 Faces

In geometry, a pentahedron (plural: pentahedra) is a polyhedron with 5 faces or sides. There are no face up-transitive polyhedra with five sides and in that location are 2 singled-out topological types.

With regular polygon faces, the two topological forms are the square pyramid and triangular prism.

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

The square pyramid tin can be seen as a triangular prism where one of its side edges (joining two squares) is complanate into a point, losing one edge and ane vertex, and changing ii squares into triangles.

Geometric variations with irregular faces can besides be constructed.

Some irregular pentahedra with 6 vertices may be called wedges.

An irregular pentahedron can be a non-convex solid: Consider a non-convex (planar) quadrilateral (such as a dart) every bit the base of the solid, and any bespeak not in the base plane as the apex.

Hosohedron [edit]

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

External links [edit]

Weisstein, Eric W. "Pentahedron". MathWorld.