Snub order-6 square tiling

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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 CDel branch hh.pngCDel split2-44.pngCDel node h.png
CDel node.pngCDel 6.pngCDel node h.pngCDel 4.pngCDel 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 tetratritetragonal tiling or 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[edit]

Drawn in chiral pairs:

H2 snub 344a.png H2 snub 344b.png

Symmetry[edit]

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}.

Uniform tiling 443-snub2.png

Related polyhedra and tiling[edit]

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 CDel branch hh.pngCDel 2a2b-cross.pngCDel nodes 01.png:

Uniform tiling 4.3.4.3.3.3.png

See also[edit]

Footnotes[edit]

References[edit]

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
  • "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.

External links[edit]