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: 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.