Rhombitriapeirogonal tiling

Rhombitriapeirogonal tiling

Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.4.∞.4
Schläfli symbol rr{∞,3} or ${\displaystyle r{\begin{Bmatrix}\infty \\3\end{Bmatrix}}}$
s2{3,∞}
Wythoff symbol 3 | ∞ 2
Coxeter diagram or
Symmetry group [∞,3], (*∞32)
[∞,3+], (3*∞)
Dual Deltoidal triapeirogonal tiling
Properties Vertex-transitive

In geometry, the rhombtriapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of rr{∞,3}.

Symmetry

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, .

Related polyhedra and tiling

Symmetry mutations

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.