Metabigyrate rhombicosidodecahedron

In geometry, the metabigyrate rhombicosidodecahedron is one of the Johnson solids ($J73 – J74 – J75$). It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron.

Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are:
 * The gyrate rhombicosidodecahedron ($C2v$) where only one cupola is rotated;
 * The parabigyrate rhombicosidodecahedron ($5.4(3.42.5) 4x2+8x4(3.4.5.4)$) where two opposing cupolae are rotated;
 * And the trigyrate rhombicosidodecahedron ($J74$) where three cupolae are rotated.