Order-6 hexagonal tiling

In geometry, the order-6 hexagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {6,6} and is self-dual.

Symmetry
This tiling represents a hyperbolic kaleidoscope of 6 mirrors defining a regular hexagon fundamental domain. This symmetry by orbifold notation is called *333333 with 6 order-3 mirror intersections. In Coxeter notation can be represented as [6*,6], removing two of three mirrors (passing through the hexagon center) in the [6,6] symmetry.

The even/odd fundamental domains of this kaleidoscope can be seen in the alternating colorings of the tiling:
 * H2 tiling 366-2.png

Related polyhedra and tiling
This tiling is topologically related as a part of sequence of regular tilings with order-6 vertices with Schläfli symbol {n,6}, and Coxeter diagram, progressing to infinity.

This tiling is topologically related as a part of sequence of regular tilings with hexagonal faces, starting with the hexagonal tiling, with Schläfli symbol {6,n}, and Coxeter diagram, progressing to infinity.