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Great hexagonal hexecontahedron

From Wikipedia, the free encyclopedia
Great hexagonal hexecontahedron
Type Star polyhedron
Face
Elements F = 60, E = 180
V = 104 (χ = −16)
Symmetry group I, [5,3]+, 532
Index references DU64
dual polyhedron Great snub dodecicosidodecahedron
3D model of a great hexagonal hexecontahedron

In geometry, the great hexagonal hexecontahedron (or great astroid ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the uniform great snub dodecicosidodecahedron. It is partially degenerate, having coincident vertices, as its dual has coplanar pentagrammic faces.

Proportions

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The faces are nonconvex hexagons. Denoting the golden ratio by , the hexagons have one angle of , one of , and four angles of . They have two long edges, two of medium length and two short ones. If the long edges have length , the medium 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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