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 Polyhedra
Famous quotes containing the word examples:
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (15331592)