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Small rhombihexacron

From Wikipedia, the free encyclopedia
Small rhombihexacron
Type Star polyhedron
Face
Elements F = 24, E = 48
V = 18 (χ = −6)
Symmetry group Oh, [4,3], *432
Index references DU18
dual polyhedron Small rhombihexahedron
3D model of a small rhombihexacron

In geometry, the small rhombihexacron (or small dipteral disdodecahedron) is the dual of the small rhombihexahedron. It is visually identical to the small hexacronic icositetrahedron. Its faces are antiparallelograms formed by pairs of coplanar triangles.

Proportions

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Each antiparallelogram has two angles of and two angles of . The diagonals of each antiparallelogram intersect at an angle of . The dihedral angle equals . The ratio between the lengths of the long edges and the short ones equals .

References

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  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
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Weisstein, Eric W. "Small rhombihexacron". MathWorld.