Gyrate rhombicosidodecahedron

In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids (J72). It is also a canonical polyhedron. It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees. They have the same faces around each vertex, but vertex configurations along the rotation become a different order, 3.4.4.5. Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are: The parabigyrate rhombicosidodecahedron (J_73) where two opposing cupolae are rotated; The metabigyrate rhombicosidodecahedron (J_74) where two non-opposing cupolae are rotated; And the trigyrate rhombicosidodecahedron (J_75) where three cupolae are rotated.