Metagyrate diminished rhombicosidodecahedron

In geometry, the metagyrate diminished rhombicosidodecahedron is one of the Johnson solids (J₇₈). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees, and a non-opposing pentagonal cupola removed. (The cupolae cannot be adjacent.)

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.