Wedge (geometry)

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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.

Properties

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.Template:R. A prismatoid is defined as a polyhedron where its vertices lie on two parallel planes, with its lateral faces are triangles, trapezoids, and parallelograms;Template:R the wedge is an example of prismatoid because of its top edge is parallel to the rectangular base.Template:R The volume of a wedge is $V = b h (\frac{a}{3} + \frac{c}{6}),$ where the base rectangle is $a$ by $b$ , $c$ is the apex edge length parallel to $a$ , and $h$ is the height from the base rectangle to the apex edge.Template:R

Examples

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.Template:R

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.

Special cases
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.