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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“He may be a very nice man. But I haven’t got the time to figure that out. All I know is, he’s got a uniform and a gun and I have to relate to him that way. That’s the only way to relate to him because one of us may have to die.”
—James Baldwin (1924–1987)