Snub order-6 square tiling

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}.

Snub order-6 square tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration3.3.3.4.3.4
Schläfli symbols(4,4,3)
s{4,6}
Wythoff symbol| 4 4 3
Coxeter diagram
Symmetry group[(4,4,3)]+, (443)
[6,4+], (4*3)
DualOrder-4-4-3 snub dual tiling
PropertiesVertex-transitive

Images

Drawn in chiral pairs:

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}.

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 :

See also

Footnotes

    References

    • 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.
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