Trigyrate rhombicosidodecahedron
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| 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 | - |
| Properties | convex |
In geometry, the Trigyrate rhombicosidodecahedron is one of the Johnson solids (J75). 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.
The 92 Johnson solids were named and described by Norman Johnson in 1966.
[edit] References
- Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Contains the original enumeration of the 92 solids and the conjecture that there are no others.
- Victor A. Zalgaller (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. No ISBN. The first proof that there are only 92 Johnson solids.
