Set of pyramidal frusta
Faces	n trapezoids, 2 n-agon
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

$V\; =\backslash frac\{1\}\{3\}\; h(B1+\backslash sqrt\{B1\backslash times\; B2\}+B2)$

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. (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

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• http://www.gomath.com/geometry/frustcone.php
• http://mathworld.wolfram.com/PyramidalFrustum.html

Polyhedra | Prismatoid polyhedra

Frustum | Tronc (géométrie)