In geometry, the gyrate rhombicosidodecahedron is one of the Johnson solids (). It is also a canonical polyhedron. Related 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, . Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are: The parabigyrate rhombicosidodecahedron () where two opposing cupolae are rotated; The metabigyrate rhombicosidodecahedron () where two non-opposing cupolae are rotated; And the trigyrate rhombicosidodecahedron () where three cupolae are rotated. External links Johnson solids