# Wedge (geometry)

In geometry, a wedge is a polyhedral solid 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.

A wedge can be considered a degenerate digonal cupola with a top face collapsed into an 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.

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 :$V = frac\left\{1\right\}\left\{6\right\} b h \left(2a+c\right)$ 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.

References

* Harris, J. W. and Stocker, H. Wedge. §4.5.2 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 101, 1998.

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