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.
Family of bifrusta | |
---|---|
Faces | 2 n-gons 2n trapezoids |
Edges | 5n |
Vertices | 3n |
Symmetry group | Dnh, [n,2], (*n22) |
Surface area | |
Volume | |
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.
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] and [3]
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 |