Great deltoidal hexecontahedron

Great deltoidal hexecontahedron
Type Star polyhedron
Face
Elements F = 60, E = 120
V = 62 (χ = 2)
Symmetry group Ih, [5,3], *532
Index references DU67
dual polyhedron Nonconvex great rhombicosidodecahedron

In geometry, the great deltoidal hexecontahedron (or great sagittal ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the nonconvex great rhombicosidodecahedron. It is visually identical to the great rhombidodecacron. It has 60 intersecting cross quadrilateral faces, 120 edges, and 62 vertices. Its faces are darts. Part of each dart lies inside the solid, hence is invisible in solid models.

3D model of a great deltoidal hexecontahedron

It is also called a great strombic hexecontahedron.

Proportions

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The darts have two angles of  , one of   and one of  . The dihedral angle equals  . The ratio between the lengths of the long and short edges is  .

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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