Bifrustum
Family 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) |
Surface area | |
Volume | |
Dual polyhedron | Elongated bipyramids |
Properties | convex |
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.[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] and [3] Note that the volume V is twice the volume of a frusta.
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
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- triakis tetrahedron
- rhombic dodecahedron
- triakis octahedron
- tetrakis hexahedron
- deltoidal icositetrahedron
- disdyakis dodecahedron
- pentagonal icositetrahedron
- rhombic triacontahedron
- triakis icosahedron
- pentakis dodecahedron
- deltoidal hexecontahedron
- disdyakis triacontahedron
- pentagonal hexecontahedron
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duals: |
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- pyramids
- truncated trapezohedra
- gyroelongated bipyramid
- cupola
- bicupola
- frustum
- bifrustum
- rotunda
- birotunda
- prismatoid
- scutoid
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