In geometry, there are seven uniform and uniform dual polyhedra named as ditrigonal.
There are five uniform ditrigonal polyhedra, all with icosahedral symmetry.[1]
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 (p.q)3 with a symmetry of order 3. Here, term ditrigonal refers to a hexagon having a symmetry of order 3 (triangular symmetry) acting with 2 rotational orbits on the 6 angles of the vertex figure (the word ditrigonal means "having two sets of 3 angles").[2]
| Type | Small ditrigonal icosidodecahedron | Ditrigonal dodecadodecahedron | Great ditrigonal icosidodecahedron | |
|---|---|---|---|---|
| Image | ||||
| Vertex figure | ||||
| Vertex configuration | 3..3..3. | 5..5..5. | (3.5.3.5.3.5)/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 |
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.