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 (J₅) rotated through 36 degrees, and a non-opposing pentagonal cupola removed. (The cupolae cannot be adjacent.)

Metagyrate diminished rhombicosidodecahedron
Type	Johnson J77 – J78 – J79
Faces	3+6×2 triangles 3+11×2 squares 3+4×2 pentagons 1 decagon
Edges	105
Vertices	55
Vertex configuration	5×2(4.5.10) 5×2(3.42.5) 3+16×2(3.4.5.4)
Symmetry group	Cs
Dual polyhedron	-
Properties	convex
Net

A Johnson solid is one of 92 strictly convex polyhedra that is composed of regular polygon faces but are not uniform polyhedra (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.^[1]