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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	, (*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

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Symmetry: , (*433)							, (433)
h{8,3} t0(4,3,3)	r{3,8}/2 t0,1(4,3,3)	h{8,3} t1(4,3,3)	h2{8,3} t1,2(4,3,3)	{3,8}/2 t2(4,3,3)	h2{8,3} t0,2(4,3,3)	t{3,8}/2 t0,1,2(4,3,3)	s{3,8}/2 s(4,3,3)
Uniform duals
V(3.4)	V3.8.3.8	V(3.4)	V3.6.4.6	V(3.3)	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 =	Spherical	Euclidean	Compact Hyperbolic			Paracompact
	*233 =	*333 =	*433 =	*533 =	*633... =	*∞33 =
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

v t e Tessellation
Periodic Pythagorean Rhombille Schwarz triangle Rectangle Domino Uniform tiling and honeycomb Coloring Convex Kisrhombille Wallpaper group Wythoff
Aperiodic Ammann–Beenker Aperiodic set of prototiles List Einstein problem Socolar–Taylor Gilbert Penrose Pinwheel Quaquaversal Rep-tile and Self-tiling Sphinx Socolar Truchet
Other Anisohedral and Isohedral Architectonic and catoptric Circle Limit III Computer graphics Honeycomb Isotoxal List Packing Pentagonal Problems Domino Wang Heesch's Squaring Dividing a square into similar rectangles Prototile Conway criterion Girih Regular Division of the Plane Regular grid Substitution Voronoi Voderberg
By vertex type Spherical 2 3.n V3.n 4.n V4.n Regular 2 3 4 6 Semi- regular 3.4.3.4 V3.4.3.4 3.4 3.∞ 3.6 V3.6 3.4.6.4 (3.6) 3.12 4.∞ 4.6.12 4.8 Hyper- bolic 3.4.3.5 3.4.3.6 3.4.3.7 3.4.3.8 3.4.3.∞ 3.5.3.5 3.5.3.6 3.6.3.6 3.6.3.8 3.7.3.7 3.8.3.8 3.4.3.4 3.∞.3.∞ 3.7 3.8 3.∞ 3.4 3 3 3 (3.4) (3.4) 3.4.6.4 3.4.7.4 3.4.8.4 3.4.∞.4 3.6.4.6 (3.7) (3.8) 3.14 3.16 3.∞ 4.5.4 4.6.4 4.7.4 4.8.4 4.∞.4 4 4 4 4 4 (4.5) (4.6) 4.6.12 4.6.14 V4.6.14 4.6.16 V4.6.16 4.6.∞ (4.7) (4.8) 4.8.10 V4.8.10 4.8.12 4.8.14 4.8.16 4.8.∞ 4.10 4.10.12 4.12 4.12.16 4.14 4.16 4.∞ 5 5 5 5 5.4.6.4 (5.6) 5.8 5.10 5.12 6 6 6 6 6.4.8.4 (6.8) 6.8 6.10 6.12 6.16 7 7 7 7.6 7.8 7.14 8 8 8 8 8.6 8.12 8.16 ∞ ∞ ∞ ∞ ∞.6 ∞.8

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