Cantic octagonal tiling

Cantic octagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	3.6.4.6
Schläfli symbol	h2{8,3}
Wythoff symbol	4 3 | 3
Coxeter diagram	=
Symmetry group	[(4,3,3)], (*433)
Dual	Order-4-3-3 t12 dual tiling
Properties	Vertex-transitive

In geometry, the tritetratrigonal tiling or shieldotritetragonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_1,2(4,3,3). It can also be named as a cantic octagonal tiling, h₂{8,3}.

Dual tiling

Related polyhedra and tiling

Uniform (4,3,3) tilings

Symmetry: [(4,3,3)], (*433)							[(4,3,3)]+, (433)
h{8,3} t0(4,3,3)	r{3,8}1/2 t0,1(4,3,3)	h{8,3} t1(4,3,3)	h2{8,3} t1,2(4,3,3)	{3,8}1/2 t2(4,3,3)	h2{8,3} t0,2(4,3,3)	t{3,8}1/2 t0,1,2(4,3,3)	s{3,8}1/2 s(4,3,3)
Uniform duals
V(3.4)3	V3.8.3.8	V(3.4)3	V3.6.4.6	V(3.3)4	V3.6.4.6	V6.6.8	V3.3.3.3.3.4

*n33 orbifold symmetries of cantic tilings: 3.6.n.6

Symmetry *n32 [1+,2n,3] = [(n,3,3)]	Spherical	Euclidean	Compact Hyperbolic			Paracompact
	*233 [1+,4,3] = [3,3]	*333 [1+,6,3] = [(3,3,3)]	*433 [1+,8,3] = [(4,3,3)]	*533 [1+,10,3] = [(5,3,3)]	*633... [1+,12,3] = [(6,3,3)]	*∞33 [1+,∞,3] = [(∞,3,3)]
Coxeter Schläfli	= h2{4,3}	= h2{6,3}	= h2{8,3}	= h2{10,3}	= h2{12,3}	= h2{∞,3}
Cantic figure
Vertex	3.6.2.6	3.6.3.6	3.6.4.6	3.6.5.6	3.6.6.6	3.6.∞.6
Domain
Wythoff	2 3 | 3	3 3 | 3	4 3 | 3	5 3 | 3	6 3 | 3	∞ 3 | 3
Dual figure
Face	V3.6.2.6	V3.6.3.6	V3.6.4.6	V3.6.5.6	V3.6.6.6	V3.6.∞.6

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, 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

• Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
• Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
• Hyperbolic and Spherical Tiling Gallery Archived 2013-03-24 at the Wayback Machine
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch