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
Famous quotes containing the word uniform:
“The sugar maple is remarkable for its clean ankle. The groves of these trees looked like vast forest sheds, their branches stopping short at a uniform height, four or five feet from the ground, like eaves, as if they had been trimmed by art, so that you could look under and through the whole grove with its leafy canopy, as under a tent whose curtain is raised.”
—Henry David Thoreau (1817–1862)