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Wedge (geometry)

释义

Volume
Examples
References
External links

Wedge

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.

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.

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

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

{{MathWorld | urlname= Wedge | title= Wedge }}

2 : Polyhedra|Prismatoid polyhedra

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