Small hexagrammic hexecontahedron

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Small hexagrammic hexecontahedron
DU72 small hexagrammic hexecontahedron.png
Type Star polyhedron
Face DU72 facets.png
Elements F = 60, E = 180
V = 112 (χ = 8)
Symmetry group Ih, [5,3], *532
Index references DU 72
dual polyhedron Small retrosnub icosicosidodecahedron
3D model of a small hexagrammic hexecontahedron Small hexagrammic hexecontahedron.stl
3D model of a small hexagrammic hexecontahedron

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.

Contents

Geometry

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.

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References