Snub order-6 square tiling

Snub order-6 square tiling
Snub order-6 square tiling Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	3.3.3.4.3.4
Schläfli symbol	s(4,4,3) s{4,6}
Wythoff symbol	| 4 4 3
Coxeter diagram	File:CDel branch hh.pngFile:CDel split2-44.pngFile:CDel node h.png File:CDel node.pngFile:CDel 6.pngFile:CDel node h.pngFile:CDel 4.pngFile:CDel node h.png
Symmetry group	[(4,4,3)]+, (443) [6,4+], (4*3)
Dual	Order-4-4-3 snub dual tiling
Properties	Vertex-transitive

In geometry, the snub order-6 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of s{(4,4,3)} or s{4,6}.

Images

File:H2 snub 344a.png File:H2 snub 344b.png

Symmetry

The symmetry is doubled as a snub order-6 square tiling, with only one color of square. It has Schläfli symbol of s{4,6}.

File:Uniform tiling 443-snub2.png

Related polyhedra and tiling

The vertex figure 3.3.3.4.3.4 does not uniquely generate a uniform hyperbolic tiling. Another with quadrilateral fundamental domain (3 2 2 2) and 2*32 symmetry is generated by File:CDel branch hh.pngFile:CDel 2a2b-cross.pngFile:CDel nodes 01.png:

File:Uniform tiling 4.3.4.3.3.3.png

See also

• Square tiling
• Uniform tilings in hyperbolic plane
• List of regular polytopes

References

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)

External links

• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch