In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids ( J75 ). 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: J72 ) where one cupola is rotated; J73 ) where two opposing cupolae are rotated; J74 ) where two non-opposing cupolae are rotated.