Frustum
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| Set of pyramidal frusta | |
|---|---|
| |
| Faces | n trapezoids, 2 n-agon |
| Edges | 3n |
| Vertices | 2n |
| Symmetry group | Cnv |
| Dual polyhedron | |
| Properties | convex |
Pyramidal frusta are a subclass of the prismatoids.
The formula for the volume of the frustum is
- [V =\frac h(B1+\sqrt+B2)]
where h is the height from the top base to the bottom base, B1 is the area of the bottom base, and B2 is the area of the top base. (See also: Heronian mean.) A more intuitive formula is: the volume of the cone (or other figure) before you chopped the top off, minus the volume of the cone (or other figure) that you chopped off.An example of a pyramidal frustum may be seen on the reverse of the Great Seal of the United States, as on the back of the U.S. one-dollar bill. The "unfinished pyramid" is surmounted by the "Eye of Providence".
Certain ancient Native American mounds also form the frustum of a pyramid.
The focal field of a still or video camera forms a frustum. In 3D computer graphics, this is called the viewing frustum.
The spelling frustrum, listed as "erroneous" by the Oxford English Dictionary, is frequently encountered and might be considered a variant. The OED gives both frusta and frustums for the plural.
External links
- http://www.gomath.com/geometry/frustcone.php
- http://mathworld.wolfram.com/PyramidalFrustum.html
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