Rhombitriapeirogonal tiling

In geometry, the rhombtriapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of rr{∞,3}. This tiling has [∞,3], (∞32) symmetry. There is only one uniform coloring. Similar to the Euclidean rhombitrihexagonal tiling, by edge-coloring there is a half symmetry form (3∞) orbifold notation. The apeireogons can be considered as truncated, t{∞} with two types of edges. It has Coxeter diagram , Schläfli symbol s2{3,∞}. The squares can be distorted into isosceles trapezoids. In the limit, where the rectangles degenerate into edges, an infinite-order triangular tiling results, constructed as a snub triapeirotrigonal tiling, . This hyperbolic tiling is topologically related as a part of sequence of uniform cantellated polyhedra with vertex configurations (3.4.n.4), and [n,3] Coxeter group symmetry.