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Great rhombidodecacron

From Wikipedia, the free encyclopedia
Great rhombidodecacron
Type Star polyhedron
Face
Elements F = 60, E = 120
V = 42 (χ = −18)
Symmetry group Ih, [5,3], *532
Index references DU73
dual polyhedron Great rhombidodecahedron
3D model of a great rhombidodecacron

In geometry, the great rhombidodecacron (or Great dipteral ditriacontahedron) is a nonconvex isohedral polyhedron. It is the dual of the great rhombidodecahedron. It is visually identical to the great deltoidal hexecontahedron. Its faces are antiparallelograms.

Proportions

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Each antiparallelogram has two angles of and two angles of . The diagonals of each antiparallelogram intersect at an angle of . The dihedral angle equals . The ratio between the lengths of the long edges and the short ones equals , which is the golden ratio. Part of each face lies inside the solid, hence is invisible in solid models.

References

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  • Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208 p. 88
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