Pentahedron

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

In geometry, a pentahedron (pl.: pentahedra) is a polyhedron with five faces or sides. There are no face-transitive polyhedra with five sides, and there are two distinct topological types. Notable polyhedra with regular polygon faces are:

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  Square pyramid with four triangles and one square. Pyramids with any quadrilateral base have the same number of faces.
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  Triangular prism with three rectangles and two triangular bases. In the case of a right triangular prism, it is a special case of wedge (geometry) with connecting parallel edges between triangles; the wedge generally has two triangles and three quadrilateral faces.
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Concave

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

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". MathWorld.