Gyrate bidiminished rhombicosidodecahedron

In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids ($J81 – J82 – J83$).

It can be constructed as a rhombicosidodecahedron with two non-opposing pentagonal cupolae ($Cs$) removed and a third is rotated 36 degrees. Related Johnson solids are:
 * The diminished rhombicosidodecahedron ($10.2(4.5.10) 5x2(3.42.5) 4+8.2(3.4.5.4)$) where one cupola is removed,
 * The parabidiminished rhombicosidodecahedron ($J82$) where two opposing cupolae are removed,
 * The metabidiminished rhombicosidodecahedron ($J5$) where two non-opposing cupolae are removed,
 * And the tridiminished rhombicosidodecahedron ($J76$) where three cupolae are removed.