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:
“The maples
Stood uniform in buckets, and the steam
Of sap and snow rolled off the sugarhouse.”
—Robert Frost (1874–1963)