Bifrustum
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.
Set of bifrusta | |
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![]() 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 |
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.[1]
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 Al, total area A and volume V are:[2]
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 |
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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 |
References
- "Octagonal Bifrustum". etc.usf.edu. Retrieved 2022-06-16.
- "Regelmäßiges Bifrustum - Rechner". RECHNERonline (in German). Retrieved 2022-06-30.
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