Truncated order-6 square tiling
In geometry, the truncated order-6 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{4,6}. The dual tiling represents the fundamental domains of the 443 orbifold symmetry. There are two reflective subgroup kaleidoscopic constructed from [(4,4,3)] by removing one or two of three mirrors. In these images fundamental domains are alternately colored black and cyan, and mirrors exist on the boundaries between colors. A larger subgroup is constructed [(4,4,3)], index 6, as (3*22) with gyration points removed, becomes (*222222). The symmetry can be doubled as 642 symmetry by adding a mirror bisecting the fundamental domain. From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular order-4 hexagonal tiling. Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms.
