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:
“Ive always been impressed by the different paths babies take in their physical development on the way to walking. Its rare to see a behavior that starts out with such wide natural variation, yet becomes so uniform after only a few months.”
—Lawrence Kutner (20th century)