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

Famous quotes containing the word uniform:

    Odors from decaying food wafting through the air when the door is opened, colorful mold growing between a wet gym uniform and the damp carpet underneath, and the complete supply of bath towels scattered throughout the bedroom can become wonderful opportunities to help your teenager learn once again that the art of living in a community requires compromise, negotiation, and consensus.
    Barbara Coloroso (20th century)