Bifrustum

In geometry, 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: and $${\displaystyle {\begin{aligned}A_{l}&=n(a b){\sqrt {\left({\tfrac {a-b}{2}}\cot {\tfrac {\pi }{n}}\right)^{2} h^{2}}}\\[4pt]A&=A_{l} n{\frac {b^{2}}{2\tan {\frac {\pi }{n}}}}\\[4pt]V&=n{\frac {a^{2} b^{2} ab}{6\tan {\frac {\pi }{n}}}}h\end{aligned}}}$$ Note that the volume V is twice the volume of a frusta.

Forms

Three bifrusta are duals to three Johnson solids, J_14-16. In general, a n-agonal bifrustum has 2n trapezoids, 2 n-agons, and is dual to the elongated dipyramids.

References