Great rhombic triacontahedron

Great rhombic triacontahedron
Type	Star polyhedron
Face
Elements	F = 30, E = 60 V = 32 (χ = 2)
Symmetry group	Ih, [5,3], *532
Index references	DU54
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). It has 30 intersecting rhombic faces.

The great rhombic triacontahedron can be constructed by expanding the size of the faces of a rhombic triacontahedron by a factor of $\varphi ^{3}=1+2\varphi =2+{\sqrt {5}}\!$, where $\varphi \!$ is the golden ratio.

References

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

External links

• Weisstein, Eric W. "Great rhombic triacontahedron". MathWorld.
• Uniform polyhedra and duals