| Parabigyrate rhombicosidodecahedron | |
|---|---|
 | |
| Type | Johnson J72 – J73 – J74 |
| Faces | 2×10 triangles 3×10 squares 2+10 pentagons |
| Edges | 120 |
| Vertices | 60 |
| Vertex configuration | 20(3.42.5) 2×10+20(3.4.5.4) |
| Symmetry group | D5d |
| Dual polyhedron | - |
| Properties | convex, canonical |
| Net | |
 | |
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.
A Johnson solid is one of 92 strictly convex polyhedra that are 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.
