Paragyrate diminished rhombicosidodecahedron

In geometry, the paragyrate diminished rhombicosidodecahedron is one of the Johnson solids (J₇₇). It can be constructed as a rhombicosidodecahedron with one pentagonal cupola rotated through 36 degrees, and the opposing pentagonal cupola removed.

Paragyrate diminished rhombicosidodecahedron
Type	Johnson J76 – J77 – J78
Faces	3x5 triangles 3x5+10 squares 1+2x5 pentagons 1 decagon
Edges	105
Vertices	55
Vertex configuration	10(4.5.10) 10(3.42.5) 3x5+2.10(3.4.5.4)
Symmetry group	C5v
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]