Related Polyhedra and Tilings
This tiling is topologically related as a part of sequence of polyhedra of pentagons with face configurations (V3.3.3.3.n). (The sequence progresses into tilings the hyperbolic plane to any n.) These face-transitive figures have (n32) rotational symmetry.
| Symmetry | 232 + D3 |
332 + T |
432 + O |
532 + I |
632 + P6 |
732 + |
832 + |
|---|---|---|---|---|---|---|---|
| Order | 6 | 12 | 24 | 60 | ∞ | ||
| Snub figure |
3.3.3.3.2 |
3.3.3.3.3 |
3.3.3.3.4 |
3.3.3.3.5 |
3.3.3.3.6 |
3.3.3.3.7 |
3.3.3.3.8 |
| Coxeter Schläfli |
s{2,3} |
s{3,3} |
s{4,3} |
s{5,3} |
s{6,3} |
s{7,3} |
s{8,3} |
| Snub dual figure |
V3.3.3.3.2 |
V3.3.3.3.3 |
V3.3.3.3.4 |
V3.3.3.3.5 |
V3.3.3.3.6 |
V3.3.3.3.7 |
|
| Coxeter | |||||||
The floret pentagonal tiling is a part of a set of uniform dual tilings, corresponding to the dual of the truncated snub hexagonal tiling.
| Wythoff | 3 | 6 2 | 2 3 | 6 | 2 | 6 3 | 2 6 | 3 | 6 | 3 2 | 6 3 | 2 | 6 3 2 | | | 6 3 2 | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Schläfli | {6,3} | t0,1{6,3} | t1{6,3} | t1,2{6,3} | t2{6,3} | t0,2{6,3} | t0,1,2{6,3} | s{6,3} | h0{6,3} | h1,2{6,3} | |
| Coxeter | |||||||||||
| Image Vertex figure |
6.6.6 |
3.12.12 |
3.6.3.6 |
6.6.6 |
{36} |
3.4.6.4 |
4.6.12 |
3.3.3.3.6 |
(3.3)3 |
3.3.3.3.3.3 |
|
| Uniform duals | |||||||||||
| Coxeter | |||||||||||
| Image Vertex figure |
V6.6.6 |
V3.12.12 |
V3.6.3.6 |
V6.6.6 |
V3.3.3.3.3.3 |
V3.4.6.4 |
V4.6.12 |
V3.3.3.3.6 |
V(3.3)3 |
||
Read more about this topic: Floret Pentagonal Tiling
Famous quotes containing the word related:
“Perhaps it is nothingness which is real and our dream which is non-existent, but then we feel think that these musical phrases, and the notions related to the dream, are nothing too. We will die, but our hostages are the divine captives who will follow our chance. And death with them is somewhat less bitter, less inglorious, perhaps less probable.”
—Marcel Proust (1871–1922)