Nonconvex Examples
Coxeter, H.S.M. et al. (1954) also classify certain star polyhedra having the same characteristics as being quasiregular:
Two are based on dual pairs of regular Kepler–Poinsot solids, in the same way as for the convex examples.
The great icosidodecahedron and the dodecadodecahedron :
| Regular | Dual regular | Quasiregular | Vertex figure |
|---|---|---|---|
great stellated dodecahedron {5/2,3}
|
great icosahedron {3,5/2}
|
Great icosidodecahedron 2 | 3 5/2 |
3.5/2.3.5/2 |
Small stellated dodecahedron {5/2,5}
|
Great dodecahedron {5,5/2}
|
Dodecadodecahedron 2 | 5 5/2 |
5.5/2.5.5/2 |
Lastly there are three ditrigonal forms, whose vertex figures contain three alternations of the two face types:
| Polyhedron | Vertex figure |
|---|---|
Ditrigonal dodecadodecahedron 3 | 5/3 5 |
(5.5/3)3 |
Small ditrigonal icosidodecahedron 3 | 5/2 3 |
(3.5/2)3 |
Great ditrigonal icosidodecahedron 3/2 | 3 5 |
((3.5)3)/2 |
Read more about this topic: Quasiregular Polyhedron
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