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Wedge | |
---|---|

Faces | 2 triangles, 3 quadrilaterals |

Edges | 9 |

Vertices | 6 |

Dual polyhedron | trigonal bipyramid |

Properties | convex |

In solid geometry, a **wedge** is a polyhedron defined by two triangles and three trapezoid faces. A wedge has five faces, nine edges, and six vertices.

A wedge is a subclass of the prismatoids with the base and opposite ridge in two parallel planes.

A wedge can also be classified as a digonal cupola.

Comparisons:

- A wedge is a parallelepiped where a face has collapsed into a line.
- A quadrilaterally-based pyramid is a wedge in which one of the edges between two trapezoid faces has collapsed into a point.

For a rectangle based wedge, the volume is

where the base rectangle is *a* by *b*, *c* is the apex edge length parallel to *a*, and *h* the height from the base rectangle to the apex edge.

Wedges can be created from decomposition of other polyhedra. For instance, the dodecahedron can be divided into a central cube with 6 wedges covering the cube faces. The orientations of the wedges are such that the triangle and trapezoid faces can connect and form a regular pentagon.

A triangular prism is a special case wedge with the two triangle faces being translationally congruent.

Two obtuse wedges can be formed by bisecting a regular tetrahedron on a plane parallel to two opposite edges.

Triangular prism (Parallel triangle wedge) |
Obtuse wedge as a bisected regular tetrahedron |
A wedge constructed from 8 triangular faces and 2 squares. It can be seen as a tetrahedron augmented by two square pyramids. |
The regular dodecahedron can be decomposed into a central cube and 6 wedges over the 6 square faces. |

- Harris, J. W., & Stocker, H. "Wedge". §4.5.2 in
*Handbook of Mathematics and Computational Science*. New York: Springer, p. 102, 1998. ISBN 978-0-387-94746-4

- Weisstein, Eric W. "Wedge".
*MathWorld*.