In geometry, the hexaoctagonal tiling is a uniform tiling of the hyperbolic plane.
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 4 points, [8,6,1<sup>+</sup>], gives [(8,8,3)], (*883). Removing the mirror between the order 2 and 8 points, [1<sup>+</sup>,8,6], gives [(4,6,6)], (*664). Removing two mirrors as [8,1<sup>+</sup>,6,1<sup>+</sup>], leaves remaining mirrors (*4343).
| Uniform Coloring | |||||
|---|---|---|---|---|---|
| Symmetry | [8,6] (*862) | [(8,3,8)] = [8,6,1<sup>+</sup>] (*883) | [(6,4,6)] = [1<sup>+</sup>,8,6] (*664) | [1<sup>+</sup>,8,6,1<sup>+</sup>] (*4343) | |
| Symbol | r | r | r | ||
| Coxeter diagram | = | = | = |
The dual tiling has face configuration V6.8.6.8, and represents the fundamental domains of a quadrilateral kaleidoscope, orbifold (*4343), shown here. Adding a 2-fold gyration point at the center of each rhombi defines a (2*43) orbifold. These are subsymmetries of [8,6].