Set of pyramidal frusta | |
---|---|
220px | |
Faces | n trapezoids, 2 n-agon |
Edges | 3n |
Vertices | 2n |
Symmetry group | C_{nv} |
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
- $ V =\frac{1}{3} h(B1+\sqrt{B1\times B2}+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. 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.