Snub order-6 square tiling

Snub tetratritetragonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex figure3.3.3.4.3.4
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

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

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}.

Related polyhedra and tiling

The vertex figure 3.3.3.4.3.4 does not not uniquely generate a uniform hyperbolic tiling. Another with quadrilateral fundamental domain (3 2 2 2) and 2*32 symmetry is generated by :

Uniform (4,4,3) tilings
Symmetry: [(4,4,3)] (*443) [(4,4,3)]+
(443)		 [(4,4,3+)]
(3*22)		 [(4,1+,4,3)]
(*3232)
h{6,4}
t0{(4,4,3)}
{(4,4,3)}		 h2{6,4}
t0,1{(4,4,3)}
r{(3,4,4)}		 {4,6}
t1{(4,4,3)}
{(4,3,4)}		 h2{6,4}
t1,2{(4,4,3)}
r{(4,4,3)}		 h{6,4}
t2{(4,4,3)}
{(3,4,4)}		 r{6,4}
t0,2{(4,4,3)}
r{(4,3,4)}		 t{4,6}
t0,1,2{(4,4,3)}
t{(4,3,4)}		 s{4,6}
 
s{(4,4,3)}		 hr{6,4}
 
hr{(4,3,4)}		 h{4,6}
 
h{(4,3,4)}		 q{4,6}
 
h2{(4,3,4)}
Uniform duals
V(3.4)4 V3.8.4.8 V(4.4)3 V3.8.4.8 V(3.4)4 V4.6.4.6 V6.8.8 V3.3.3.4.3.4 V(4.4.3)2 V66 V4.3.4.6.6
Uniform tetrahexagonal tilings
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
V64 V4.12.12 V(4.6)2 V6.8.8 V46 V4.4.4.6 V4.8.12
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}

References

See also

External links