# Wedge (geometry)

In

geometry , a**wedge**is a polyhedral solid defined by twotriangle s and threetrapezoid faces. A wedge has five faces, nine edges, and six vertices.A wedge is a subclass of the

prismatoid s.A wedge can be considered a degenerate

digon al 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 centralcube 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 regularpentagon .A

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

* A wedge is aparallelepiped where a face has collapsed into a line.

* A quadrilaterally-basedpyramid 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 :$V\; =\; frac\{1\}\{6\}\; b\; h\; (2a+c)$ 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.**External links***

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