Rhombitriapeirogonal tiling
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 ,
Paracompact uniform tilings in [∞,3] family
Symmetry: [∞,3], (*∞32)
[∞,3]+
[1+ ,∞,3]
[∞,3+ ]
{∞,3}
t{∞,3}
r{∞,3}
t{3,∞}
{3,∞}
rr{∞,3}
tr{∞,3}
sr{∞,3}
h{∞,3}
h2 {∞,3}
s{3,∞}
Uniform duals
V∞3
V3.∞.∞
V(3.∞)2
V6.6.∞
V3∞
V4.3.4.∞
V4.6.∞
V3.3.3.3.∞
V(3.∞)3
V3.3.3.3.3.∞
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.
*n 32 symmetry mutation of expanded tilings: 3.4.n .4
Symmetryn 32
Spherical
Euclid.
Compact hyperb.
Paraco.
Noncompact hyperbolic
*232
*332
*432
*532
*632
*732
*832
*∞32
Figure
Config.
3.4.2.4
3.4.3.4
3.4.4.4
3.4.5.4
3.4.6.4
3.4.7.4
3.4.8.4
3.4.∞.4
3.4.12i.4
3.4.9i.4
3.4.6i.4
See also
References
External links
