Frustum
From Wikipedia, the free encyclopedia
| Set of pyramidal frusta | |
|---|---|
 |
|
| Faces | n trapezoids, 2 n-gon |
| Edges | 3n |
| Vertices | 2n |
| Symmetry group | Cnv |
| Dual polyhedron | - |
| Properties | convex |
A frustum is the portion of a solid – normally a cone or pyramid – which lies between two parallel planes cutting the solid. Degenerate cases are obtained for finite solids by cutting with a single plane only.
Pyramidal frusta are a subclass of the prismatoids.
The formula for the volume of the frustum is
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 sliced the top off, minus the volume of the cone (or other figure) that you sliced off:
The result comes from 
and 
.
Two frusta joined at their bases make a bifrustum.
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 Oxford English Dictionary gives both frusta and frustums for the plural.
