Quasiregular Polyhedra - Nonconvex Examples

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}


3 | 2 5/2


great icosahedron
{3,5/2}


5/2 | 2 3


Great icosidodecahedron


2 | 3 5/2

3.5/2.3.5/2

Small stellated dodecahedron
{5/2,5}


5 | 2 5/2


Great dodecahedron
{5,5/2}


5/2 | 2 5


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 (1533–1592)