Bifrustum

In geometry, an Template:Mvar-agonal bifrustum is a polyhedron composed of three parallel planes of [[polygon|Template:Mvar-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 Template:Mvar-gonal bifrustum with the equatorial polygon sides Template:Mvar, bases sides Template:Mvar and semi-height (half the distance between the planes of bases) Template:Mvar, the lateral surface area Template:Mvar, total area Template:Mvar and volume Template:Mvar are: and $$\begin{array}{rl}{A}_l& =n(a+b)\sqrt{{(\frac{a-b}{2}\cot \frac{\pi }{n})}^2+h^2}\\ A& =A_l+n\frac{b^2}{2\tan \frac{\pi }{n}}\\ V& =n\frac{a^2+b^2+ab}{6\tan \frac{\pi }{n}}h\end{array}$$ 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 Template:Mvar-agonal bifrustum has 2n trapezoids, 2 Template:Mvar-agons, and is dual to the elongated dipyramids.

Triangular bifrustum	Square bifrustum	Pentagonal bifrustum
File:Dual elongated triangular dipyramid.png	File:Dual elongated square dipyramid.png	File:Dual elongated pentagonal dipyramid.png
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