Trigyrate rhombicosidodecahedron



In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids ($J74 – J75 – J76$). It contains 20 triangles, 30 squares and 12 pentagons. It is also a canonical polyhedron.

It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae rotated through 36 degrees. Related Johnson solids are:
 * The gyrate rhombicosidodecahedron ($C3v$) where one cupola is rotated;
 * The parabigyrate rhombicosidodecahedron ($5x6(3.42.5) 4x3+3x6(3.4.5.4)$) where two opposing cupolae are rotated;
 * And the metabigyrate rhombicosidodecahedron ($J75$) where two non-opposing cupolae are rotated.