Parabigyrate rhombicosidodecahedron

In geometry, the parabigyrate rhombicosidodecahedron is one of the Johnson solids (J₇₃). It can be constructed as a rhombicosidodecahedron with two opposing pentagonal cupolae rotated through 36 degrees. It is also a canonical polyhedron.

Parabigyrate rhombicosidodecahedron
Type	Johnson J72 – J73 – J74
Faces	2x10 triangles 3x10 squares 2+10 pentagons
Edges	120
Vertices	60
Vertex configuration	20(3.42.5) 2x10+20(3.4.5.4)
Symmetry group	D5d
Dual polyhedron	-
Properties	convex, canonical
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]

Alternative Johnson solids, constructed by rotating different cupolae of a rhombicosidodecahedron, are:

• The gyrate rhombicosidodecahedron (J₇₂) where only one cupola is rotated;
• The metabigyrate rhombicosidodecahedron (J₇₄) where two non-opposing cupolae are rotated;
• And the trigyrate rhombicosidodecahedron (J₇₅) where three cupolae are rotated.