Truncated order-6 octagonal tiling

Truncated order-6 octagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration6.16.16
Schläfli symbolt{8,6}
Wythoff symbol2 6 | 8
Coxeter diagram
Symmetry group[8,6], (*862)
DualOrder-8 hexakis hexagonal tiling
PropertiesVertex-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)

Related polyhedra and tiling

References

See also

Wikimedia Commons has media related to Uniform tiling 6-16-16.

External links

This article is issued from Wikipedia - version of the Tuesday, November 11, 2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.