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Medial hexagonal hexecontahedron

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Medial hexagonal hexecontahedron
Type Star polyhedron
Face
Elements F = 60, E = 180
V = 104 (χ = −16)
Symmetry group I, [5,3]+, 532
Index references DU46
dual polyhedron Snub icosidodecadodecahedron
3D model of a medial hexagonal hexecontahedron

In geometry, the medial hexagonal hexecontahedron (or midly dentoid ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform snub icosidodecadodecahedron.

Proportions

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The faces of the medial hexagonal hexecontahedron are irregular nonconvex hexagons. Denote the golden ratio by , and let be the real zero of the polynomial . The number can be written as , where is the plastic ratio. Then each face has four equal angles of , one of and one of . Each face has two long edges, two of medium length and two short ones. If the medium edges have length , the long ones have length and the short ones . The dihedral angle 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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