Cantic octagonal tiling

Tritetratrigonal 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

*n33 orbifold symmetries of cantic tilings: *3.6.n.6*
Symmetry *n32 [1⁺,2n,3] = [(n,3,3)]	Spherical	Euclidean	Compact Hyperbolic			Paracompact
Symmetry *n32 [1⁺,2n,3] = [(n,3,3)]	*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

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.

Periodic

Pythagorean Rhombille Schwarz triangle Rectangle Domino Uniform tiling & honeycomb Coloring Convex Kisrhombille Wallpaper group Wythoff

Aperiodic

Ammann–Beenker Aperiodic set of prototiles List Einstein problem Socolar–Taylor Gilbert Penrose Pentagonal Pinwheel Quaquaversal Rep-tile & Self-tiling Sphinx Truchet

Other

Anisohedral & Isohedral Architectonic & catoptric Circle Limit III Computer graphics Honeycomb Isotoxal Packing Problems Domino Wang Heesch's Squaring Prototile Conway criterion Girih Regular Division of the Plane Regular grid Substitution Voronoi Voderberg

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