Wedge (geometry)
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| Wedge | |
|---|---|
 |
|
| 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
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.
[edit] References
- Harris, J. W. and Stocker, H. Wedge. §4.5.2 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 101, 1998.
