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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.
Contents
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:
Volume
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.
Examples
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.