Uniform Colorings
There are 9 distinct uniform colorings of a triangular tiling. (Naming the colors by indices on the 6 triangles around a vertex: 111111, 111112, 111212, 111213, 111222, 112122, 121212, 121213, 121314)
Four of the colorings are generated by Wythoff constructions. Seven of the nine distinct colorings can be made as reductions of the four coloring: 121314. The remaining two, 111222 and 112122, have no Wythoff constructions.
| Coloring indices |
111111 | 121212 | 121314 | 121213 |
|---|---|---|---|---|
| Coloring | ||||
| Symmetry | *632 (p6m) |
*333 (p3m1) ] = |
333 (p3) ]+ |
3*3 (p31m) |
| Wythoff symbol | 6 | 3 2 | 3 | 3 3 | | 3 3 3 | |
| Coxeter-Dynkin | = |
| Coloring indices |
111222 | 112122 | 111112 | 111212 | 111213 |
|---|---|---|---|---|---|
| Coloring | |||||
| Symmetry | 2*22 (cmm) |
2222 (p2) + |
*333 (p3m1) ] |
*333 (p3m1) ] |
333 (p3) ]+ |
Read more about this topic: Triangular Tiling
Famous quotes containing the word uniform:
“Odors from decaying food wafting through the air when the door is opened, colorful mold growing between a wet gym uniform and the damp carpet underneath, and the complete supply of bath towels scattered throughout the bedroom can become wonderful opportunities to help your teenager learn once again that the art of living in a community requires compromise, negotiation, and consensus.”
—Barbara Coloroso (20th century)