| Trigyrate rhombicosidodecahedron | |
|---|---|
 | |
| Type | Johnson J74 – J75 – J76 |
| Faces | 2+2×3+2×6 triangles 4×3+3×6 squares 4×3 pentagons |
| Edges | 120 |
| Vertices | 60 |
| Vertex configuration | 5×6(3.42.5) 4×3+3×6(3.4.5.4) |
| Symmetry group | C3v |
| Dual polyhedron | - |
| Properties | convex, canonical |
| Net | |
 | |
In geometry, the trigyrate rhombicosidodecahedron is one of the Johnson solids (J75). It contains 20 triangles, 30 squares and 12 pentagons. 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]
It can be constructed as a rhombicosidodecahedron with three pentagonal cupolae rotated through 36 degrees. Related Johnson solids are:
- The gyrate rhombicosidodecahedron (J72) where one cupola is rotated;
- The parabigyrate rhombicosidodecahedron (J73) where two opposing cupolae are rotated;
- And the metabigyrate rhombicosidodecahedron (J74) where two non-opposing cupolae are rotated.
