Order-6 octagonal tiling


In geometry, the order-6 octagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of.

Symmetry

This tiling represents a hyperbolic kaleidoscope of 8 mirrors meeting at a point and bounding regular octagon fundamental domains. This symmetry by orbifold notation is called *33333333 with 8 order-3 mirror intersections. In Coxeter notation can be represented as , removing two of three mirrors in the 862 symmetry| symmetry.

Uniform constructions

There are four uniform constructions of this tiling, three of them as constructed by mirror removal from the kaleidoscope. Removing the mirror between the order 2 and 6 points, , gives ,. Removing two mirrors as , leaves remaining mirrors.
Uniform
Coloring
Symmetry

 =

=

=

Symbolr
Coxeter
diagram		 = =

Related polyhedra and tiling

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