Bifrustum

In geometry, an Template:Mvar-gonal bifrustum is a polyhedron composed of three parallel planes of [[polygon|Template:Mvar-gons]], 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: $$\begin{array}{cc}{A}_l& =n(a+b)\sqrt{{(\frac{a-b}{2}\cot \frac{\pi }{n})}^2+h^2}\\ A& =A_l+n\frac{b^2}{2\tan \frac{\pi }{n}}\\ V& =n\frac{a^2+b^2+ab}{6\tan \frac{\pi }{n}}h\end{array}$$ The volume V is twice the volume of a frustum.

Forms

Three bifrusta are duals to three Johnson solids, Template:Math. In general, an Template:Mvar-gonal bifrustum has Template:Math trapezoids, 2 Template:Mvar-gons, and is dual to the elongated dipyramids.

Triangular bifrustum	Square bifrustum	Pentagonal bifrustum
6 trapezoids, 2 triangles. Dual to elongated triangular bipyramid, Template:Math	8 trapezoids, 2 squares. Dual to elongated square bipyramid, Template:Math	10 trapezoids, 2 pentagons. Dual to elongated pentagonal bipyramid, Template:Math

External links

• Template:MathWorld