Wedge (geometry)

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This article is about the polyhedron defined by two triangles and three trapezoid faces. For the wardrobe malfunction, see Wedgie.
Wedge
Square Pyramid
Faces 2 triangles,
3 quadrilaterals
Edges 9
Vertices 6
Dual polyhedron trigonal bipyramid
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.

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 = bh\left(\frac{a}{3}+\frac{c}{6}\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.

Special cases
Triangular prism wedge.png
Triangular prism
(Parallel triangle wedge)
Tet-oct-wedge.png
A wedge constructed from 8 triangular faces and 2 squares. It can be seen as a tetrahedron augmented by two square pyramids.

References[edit]

  • Harris, J. W., & Stocker, H. "Wedge". §4.5.2 in Handbook of Mathematics and Computational Science. New York: Springer, p. 102, 1998. ISBN 978-0-387-94746-4

External links[edit]