I think I have found a novel tiling using hexagons, with octagonal symmetry, infinite inwards and outwards (at least I couldn't find it on-line). The hexagons are scaled with the ratio r = √(1+1/√2). See the measures of the hexagon in the second image (𝛕 = 2π). The hexagon can be cut in 6 similar triangles, which are 1/8 of a regular octagon. If the hexagons of the first tiling are decomposed into those triangles we get the the third image. And if some of those triangles are recombined into bigger ones, we get the fourth.
#geometry #Mathematics #tiling #hexagon #octogonal #infinity #mathart