In geometry, the tetrahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol r{6,4}.
There are for uniform constructions of this tiling, three of them as constructed by mirror removal from the [6,4] kaleidoscope. Removing the last mirror, [6,4,1<sup>+</sup>], gives [6,6], (*662). Removing the first mirror [1<sup>+</sup>,6,4], gives [(4,4,3)], (*443). Removing both mirror as [1<sup>+</sup>,6,4,1<sup>+</sup>], leaving [(3,âÂÂ,3,âÂÂ)] (*3232).
The dual tiling, called a rhombic tetrahexagonal tiling, with face configuration V4.6.4.6, and represents the fundamental domains of a quadrilateral kaleidoscope, orbifold (*3232), shown here in two different centered views. Adding a 2-fold rotation point in the center of each rhombi represents a (2*32) orbifold.