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.

Uniform colorings

The half symmetry = can be shown with alternating two colors of octagons, with as Coxeter diagram.

Symmetry

The dual tiling represents the fundamental domains of the *443 orbifold symmetry. There are two reflective subgroup kaleidoscopic constructed from 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, index 6, as with gyration points removed, becomes.
The symmetry can be doubled as 642 symmetry by adding a mirror bisecting the fundamental domain.

Related polyhedra and tilings

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.
It can also be generated from the hyperbolic tilings: