Bifrustum

Set of bifrusta
Example hexagonal bifrustum
Faces	2 n-gons, 2n trapezoids
Edges	5n
Vertices	3n
Symmetry group	Dnh, [n,2], (*n22)
Dual polyhedron	Elongated bipyramids
Properties	convex

An n-agonal bifrustum is a polyhedron composed of three parallel planes of n-agons, with the middle plane largest and usually the top and bottom congruent.

It can be constructed as two congruent frusta combined across a plane of symmetry, and also as a bipyramid with the two polar vertices truncated.

They are duals to the family of elongated bipyramids.

Formulae

For a regular n-gonal bifrustum with the equatorial polygon sides a, bases sides b and semi-height (half the distance between the planes of bases) h, the lateral surface area A_l, total area A and volume V are:

$A_{l}=n(a+b){\sqrt {\left({\frac {a-b}{2}}\cot {\frac {\pi }{n}}\right)^{2}+h^{2}}}\,,$

$A=A_{l}+n{\frac {b^{2}}{2\tan {\frac {\pi }{n}}}}\,,$

$V=n{\frac {a^{2}-b^{2}}{6\tan {\frac {\pi }{n}}}}h\,.$

Forms

Three bifrusta are duals to three Johnson solids, J14-16. In general, a n-agonal bifrustum has 2n trapezoids, 2 n-agons, and is dual to the elongated dipyramids.

Triangular bifrustum	Square bifrustum	Pentagonal bifrustum
6 trapezoids, 2 triangles. Dual to elongated triangular bipyramid, J14	8 trapezoids, 2 squares. Dual to elongated square bipyramid, J15	10 trapezoids, 2 pentagons. Dual to elongated pentagonal bipyramid, J16