In geometry, the order-6 octagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of .
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 [8*,6], removing two of three mirrors (passing through the octagon center) in the [8,6] symmetry.
There are four uniform constructions of this tiling, three of them as constructed by mirror removal from the [8,6] kaleidoscope. Removing the mirror between the order 2 and 6 points, [8,6,1<sup>+</sup>], gives [(8,8,3)], (*883). Removing two mirrors as [8,6<sup>*</sup>], leaves remaining mirrors (*444444).
| Uniform Coloring | |||||
|---|---|---|---|---|---|
| Symmetry | [8,6] (*862) | [8,6,1<sup>+</sup>] = [(8,8,3)] (*883) = | [8,1<sup>+</sup>,6] (*4232) = | [8,6<sup>*</sup>] (*444444) | |
| Symbol | r(8,6,8) | ||||
| Coxeter diagram | = | = |
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.