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From Wikipedia, the free encyclopedia
In geometry, there are seven uniform and uniform dual polyhedra named as ditrigonal.[1]
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 3/2 | 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 | 3.5⁄2.3.5⁄2.3.5⁄2 | 5.5⁄3.5.5⁄3.5.5⁄3 | (3.5.3.5.3.5)/2 |
Faces | 32 20 {3}, 12 { 5⁄2 } |
24 12 {5}, 12 { 5⁄2 } |
32 20 {3}, 12 {5} |
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.[1]
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