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Medial pentagonal hexecontahedron

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Medial pentagonal hexecontahedron
Type Star polyhedron
Face
Elements F = 60, E = 150
V = 84 (χ = −6)
Symmetry group I, [5,3]+, 532
Index references DU40
dual polyhedron Snub dodecadodecahedron

In geometry, the medial pentagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the snub dodecadodecahedron. It has 60 intersecting irregular pentagonal faces.

Proportions

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Denote the golden ratio by φ, and let be the smallest (most negative) real zero of the polynomial Then each face has three equal angles of one of and one of Each face has one medium length edge, two short and two long ones. If the medium length is 2, then the short edges have length and the long edges have length The dihedral angle equals The other real zero of the polynomial P plays a similar role for the medial inverted pentagonal hexecontahedron.

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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