# Truncated order-6 octagonal tiling

Truncated order-6 octagonal tiling Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 6.16.16
Schläfli symbol t{8,6}
Wythoff symbol 2 6 | 8
Coxeter diagram     Symmetry group [8,6], (*862)
Dual Order-8 hexakis hexagonal tiling
Properties Vertex-transitive

In geometry, the truncated order-6 octagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{8,6}.

## Uniform colorings

A secondary construction t{(8,8,3)} is called a truncated trioctaoctagonal tiling: ## Symmetry Truncated order-6 octagonal tiling with mirror lines,   The dual to this tiling represent the fundamental domains of [(8,8,3)] (*883) symmetry. There are 3 small index subgroup symmetries constructed from [(8,8,3)] 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 862 symmetry by adding a mirror bisecting the fundamental domain.

Small index subgroups of [(8,8,3)] (*883)
Index 1 2 6
Diagram    Coxeter
(orbifold)
[(8,8,3)] =   (*883)
[(8,1+,8,3)] =    =   (*4343)
[(8,8,3+)] =   (3*44)
[(8,8,3*)] =    (*444444)
Direct subgroups
Index 2 4 12
Diagram   Coxeter
(orbifold)
[(8,8,3)]+ =   (883)
[(8,8,3+)]+ =    =   (4343)
[(8,8,3*)]+ =    (444444)