# 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 ${\displaystyle \varphi ^{3}=1+2\varphi \!}$, with ${\displaystyle \varphi \!}$ being the golden ratio.