Wedge
Wedge
Faces 2 triangles,
3 quadrilaterals
Edges 9
Vertices 6
Dual polyhedron Notch
Properties convex

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.

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.

Special cases

Triangular prism
(Parallel triangle wedge)

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.

References