Parabigyrate rhombicosidodecahedron

In geometry, the parabigyrate rhombicosidodecahedron is one of the Johnson solids ($J72 – J73 – J74$). It can be constructed as a rhombicosidodecahedron with two 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 ($D5d$) where only one cupola is rotated;
 * The metabigyrate rhombicosidodecahedron ($20(3.42.5) 2x10+20(3.4.5.4)$) where two non-opposing cupolae are rotated;
 * And the trigyrate rhombicosidodecahedron ($J73$) where three cupolae are rotated.