Small hexagrammic hexecontahedron

Small hexagrammic hexecontahedron
Type Star polyhedron
Face
Elements F = 60, E = 180
V = 112 (χ = −8)
Symmetry group Ih, [5,3], *532
Index references DU72
dual polyhedron Small retrosnub icosicosidodecahedron

In geometry, the small hexagrammic hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the small retrosnub icosicosidodecahedron. It is partially degenerate, having coincident vertices, as its dual has coplanar triangular faces.

3D model of a small hexagrammic hexecontahedron

Geometry

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Its faces are hexagonal stars with two short and four long edges. Denoting the golden ratio by   and putting  , the stars have five equal angles of   and one of  . Each face has four long and two short edges. The ratio between the edge lengths is

 .

The dihedral angle equals  . Part of each face is inside the solid, hence is not visible in solid models.

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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