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}.
A secondary construction t{(8,8,3)} is called a truncated trioctaoctagonal tiling:
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.
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) |
Uniform octagonal/hexagonal tilings | ||||||
---|---|---|---|---|---|---|
Symmetry: [8,6], (*862) | ||||||
{8,6} | t{8,6} |
r{8,6} | 2t{8,6}=t{6,8} | 2r{8,6}={6,8} | rr{8,6} | tr{8,6} |
Uniform duals | ||||||
V86 | V6.16.16 | V(6.8)2 | V8.12.12 | V68 | V4.6.4.8 | V4.12.16 |
Alternations | ||||||
[1+,8,6] (*466) |
[8+,6] (8*3) |
[8,1+,6] (*4232) |
[8,6+] (6*4) |
[8,6,1+] (*883) |
[(8,6,2+)] (2*43) |
[8,6]+ (862) |
h{8,6} | s{8,6} | hr{8,6} | s{6,8} | h{6,8} | hrr{8,6} | sr{8,6} |
Alternation duals | ||||||
V(4.6)6 | V3.3.8.3.8.3 | V(3.4.4.4)2 | V3.4.3.4.3.6 | V(3.8)8 | V3.45 | V3.3.6.3.8 |