In geometry, the order-8 hexagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of .
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, [6,8,1<sup>+</sup>], gives [(6,6,4)], (*664). Removing the mirror between the order 8 and 6 points, [6,1<sup>+</sup>,8], gives (*4232). Removing two mirrors as [6,8<sup>*</sup>], leaves remaining mirrors (*33333333).
| Uniform Coloring | |||||
|---|---|---|---|---|---|
| Symmetry | [6,8] (*862) | [6,8,1<sup>+</sup>] = [(6,6,4)] (*664) = | [6,1<sup>+</sup>,8] (*4232) = | [6,8<sup>*</sup>] (*33333333) | |
| Symbol | r(8,6,8) | ||||
| Coxeter diagram | = | = |
This tiling represents a hyperbolic kaleidoscope of 4 mirrors meeting as edges of a square, with eight squares around every vertex. This symmetry by orbifold notation is called (*444444) with 6 order-4 mirror intersections. In Coxeter notation can be represented as [8,6*], removing two of three mirrors (passing through the square center) in the [8,6] symmetry.