Truncated order-6 square tiling

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).

From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular order-4 hexagonal tiling.