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In geometry, the truncated order-6 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{6,6}. It can also be identically constructed as a cantic order-6 square tiling, h2{4,6}
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Uniform colorings
By *663 symmetry, this tiling can be constructed as an omnitruncation, t{(6,6,3)}:
Symmetry
The dual to this tiling represent the fundamental domains of [(6,6,3)] (*663) symmetry. There are 3 small index subgroup symmetries constructed from [(6,6,3)] by mirror removal and alternation. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors.
The symmetry can be doubled as 662 symmetry by adding a mirror bisecting the fundamental domain.
References
Truncated order-6 hexagonal tiling Wikipedia(Text) CC BY-SA