Truncated order-6 hexagonal tiling

Truncated order-6 hexagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration6.12.12
Schläfli symbolt{6,6} or h2{4,6}
t{(6,6,3)}
Wythoff symbol2 6 | 6
3 6 6 |
Coxeter diagram =
=
Symmetry group[6,6], (*662)
[(6,6,3)], (*663)
DualOrder-6 hexakis hexagonal tiling
PropertiesVertex-transitive

In geometry, the truncated order-6 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{6,6}. It can also be identically constructed as a cantic order-6 square tiling, h2{4,6}

Uniform colorings

By *663 symmetry, this tiling can be constructed as an omnitruncation, t{(6,6,3)}:

Symmetry

Truncated order-6 hexagonal tiling with *663 mirror lines

The dual to this tiling represent the fundamental domains of [(6,6,3)] (*663) symmetry. There are 3 small index subgroup symmetries constructed from [(6,6,3)] 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 662 symmetry by adding a mirror bisecting the fundamental domain.

Small index subgroups of [(6,6,3)] (*663)
Index 1 2 6
Diagram
Coxeter
(orbifold)
[(6,6,3)] =
(*663)
[(6,1+,6,3)] = =
(*3333)
[(6,6,3+)] =
(3*33)
[(6,6,3*)] =
(*333333)
Direct subgroups
Index 2 4 12
Diagram
Coxeter
(orbifold)
[(6,6,3)]+ =
(663)
[(6,6,3+)]+ = =
(3333)
[(6,6,3*)]+ =
(333333)

Related polyhedra and tiling

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