Bigyrate diminished rhombicosidodecahedron

In geometry, the bigyrate diminished rhombicosidodecahedron is one of the Johnson solids (J₇₉). It can be constructed as a rhombicosidodecahedron with two pentagonal cupolae rotated through 36 degrees, and a third pentagonal cupola removed. (None of the cupolae can be adjacent.)

Bigyrate diminished rhombicosidodecahedron
Type	Johnson J78 – J79 – J80
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) 10×2(3.42.5) 3+11×2(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]