Ditrigonal polyhedron
In geometry, there are seven uniform and uniform dual polyhedra named as ditrigonal.
Ditrigonal vertex figures
There are five uniform ditrigonal polyhedra, all with icosahedral symmetry.The three uniform star polyhedron with Wythoff symbol of the form 3 | p q or | p q are ditrigonal, at least if p and q are not 2. Each polyhedron includes two types of faces, being of triangles, pentagons, or pentagrams. Their vertex configurations are of the form p.q.p.q.p.q or 3 with a symmetry of order 3. Here, term ditrigonal refers to a hexagon having a symmetry of order 3 acting with 2 rotational orbits on the 6 angles of the vertex figure.
| Type | Small ditrigonal icosidodecahedron | Ditrigonal dodecadodecahedron | Great ditrigonal icosidodecahedron |
| Image | |||
| Vertex figure | |||
| Vertex configuration | 3..3..3. | 5..5..5. | /2 |
| Faces | 32 20, 12 | 24 12, 12 | 32 20, 12 |
| Wythoff symbol | 3 | 5/2 3 | 3 | 5/3 5 | 3 | 3/2 5 |
| Coxeter diagram |
Other uniform ditrigonal polyhedra
The small ditrigonal dodecicosidodecahedron and the great ditrigonal dodecicosidodecahedron are also uniform.Their duals are respectively the small ditrigonal dodecacronic hexecontahedron and great ditrigonal dodecacronic hexecontahedron.