Gyrate bidiminished rhombicosidodecahedron

In geometry, the gyrate bidiminished rhombicosidodecahedron is one of the Johnson solids (J₈₂). It can be produced by removing two pentagonal cupolae and rotating a third pentagonal cupola through 36 degrees.

A Johnson solid is one of 92 strictly convex polyhedra that have regular faces but are not uniform (that is, they are not Platonic solids, Archimedean solids, prisms or antiprisms). They were named by Norman Johnson, who first listed these polyhedra in 1966.