Hexagonal Tiling - Uniform Colorings

Uniform Colorings

There are 3 distinct uniform colorings of a hexagonal tiling, all generated from reflective symmetry of Wythoff constructions. The (h,k) represent the periodic repeat of one colored tile, counting hexagonal distances as h first, and k second.

k-uniform 1-uniform 2-uniform 3-uniform
Picture
Colors 1 2 3 2 4 2 7
(h,k) (1,0) (1,1) (2,0) (2,1)
Schläfli symbol {6,3} t{3,6} t{3}
Wythoff symbol 3 | 6 2 2 6 | 3 3 3 3 |
Symmetry *632
(p6m)
 *333
(p3)
]		 *632
(p6m)
 632
(p6)
+
Coxeter-Dynkin diagram
Conway polyhedron notation H tH teH t6daH t6dateH

The 3-color tiling is a tessellation generated by the order-3 permutohedrons.

Read more about this topic:  Hexagonal Tiling

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