Triangular Tiling - Uniform Colorings

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

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