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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.

Wedge | |
---|---|

Faces | 2 triangles, 3 quadrilaterals |

Edges | 9 |

Vertices | 6 |

A wedge is a polyhedron of a rectangular base, with the faces are two isosceles triangles and two trapezoids that meet at the top of an edge.^{[1]}. A prismatoid is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces are triangles, trapezoids, and parallelograms;^{[2]} the wedge is an example of prismatoid because of its top edge is parallel to the rectangular base.^{[3]} The volume of a wedge is
where the base rectangle is by , is the apex edge length parallel to , and is the height from the base rectangle to the apex edge.^{[1]}

In some special cases, the wedge is the right prism if all edges connecting triangles are equal in length, and the triangular faces are perpendicular to the rectangular base.^{[3]}

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.

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

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. |

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^{a}^{b}Harris, J. W.; Stocker, H. (1998). ""Wedge". §4.5.2".*Handbook of Mathematics and Computational Science*. New York: Springer. p. 102. ISBN 978-0-387-94746-4. **^**Alsina, Claudi; Nelsen, Roger B. (2015),*A Mathematical Space Odyssey: Solid Geometry in the 21st Century*, Mathematical Association of America, p. 85, ISBN 978-0-88385-358-0.- ^
^{a}^{b}Haul, Wm. S. (1893).*Mensuration*. Ginn & Company. p. 45.

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