Snub tetrahexagonal tiling
Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration3.3.4.3.6
Schläfli symbolsr{6,4} or s { 6 4 } {\displaystyle s{\begin{Bmatrix}6\\4\end{Bmatrix}}}
Wythoff symbol| 6 4 2
Coxeter diagramor
Symmetry group[6,4]+, (642)
DualOrder-6-4 floret pentagonal tiling
PropertiesVertex-transitive Chiral

In geometry, the snub tetrahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{6,4}.

Images

Drawn in chiral pairs, with edges missing between black triangles:

Related polyhedra and tiling

The snub tetrahexagonal tiling is fifth in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n.

4n2 symmetry mutations of snub tilings: 3.3.4.3.n vte
Symmetry 4n2SphericalEuclideanCompact hyperbolicParacomp.
242342442542642742842∞42
Snub figures
Config.3.3.4.3.23.3.4.3.33.3.4.3.43.3.4.3.53.3.4.3.63.3.4.3.73.3.4.3.83.3.4.3.∞
Gyro figures
Config.V3.3.4.3.2V3.3.4.3.3V3.3.4.3.4V3.3.4.3.5V3.3.4.3.6V3.3.4.3.7V3.3.4.3.8V3.3.4.3.∞
Uniform tetrahexagonal tilings vte
Symmetry: [6,4], (*642) (with [6,6] (*662), [(4,3,3)] (*443) , [∞,3,∞] (*3222) index 2 subsymmetries) (And [(∞,3,∞,3)] (*3232) index 4 subsymmetry)
= = === = === = ==
{6,4}t{6,4}r{6,4}t{4,6}{4,6}rr{6,4}tr{6,4}
Uniform duals
V64V4.12.12V(4.6)2V6.8.8V46V4.4.4.6V4.8.12
Alternations
[1+,6,4] (*443)[6+,4] (6*2)[6,1+,4] (*3222)[6,4+] (4*3)[6,4,1+] (*662)[(6,4,2+)] (2*32)[6,4]+ (642)
======
h{6,4}s{6,4}hr{6,4}s{4,6}h{4,6}hrr{6,4}sr{6,4}
  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
  • "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN0-486-40919-8. LCCN.

See also

External links