Wedge (geometry)

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Wedge
Square Pyramid
Faces 2 triangles,
3 quadrilaterals
Edges 9
Vertices 6
Dual polyhedron ?
Properties convex

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{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.

Triangular prism(Parallel triangle wedge)
Enlarge
Triangular prism
(Parallel triangle wedge)

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