Great rhombic triacontahedron
|Great rhombic triacontahedron|
|Elements||F = 30, E = 60|
V = 32 (χ = 2)
|Symmetry group||Ih, [5,3], *532|
|dual polyhedron||Great icosidodecahedron|
In geometry, the great rhombic triacontahedron is a nonconvex isohedral, isotoxal polyhedron. It is the dual of the great icosidodecahedron (U54). Like the convex rhombic triacontahedron it has 30 rhombic faces, 60 edges and 32 vertices (also 20 on 3-fold and 12 on 5-fold axes).
It can be constructed from the convex solid by expanding the faces by factor of , where is the golden ratio.
This solid is to the compound of great icosahedron and great stellated dodecahedron what the convex one is to the compound of dodecahedron and icosahedron: The crossing edges in the dual compound are the diagonals of the rhombs.
- Wenninger, Magnus (1983), Dual Models, Cambridge University Press, ISBN 978-0-521-54325-5, MR 0730208
- Weisstein, Eric W. "Great rhombic triacontahedron". MathWorld.
- David I. McCooey: animation and measurements
- Uniform polyhedra and duals
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