Cantic order-4 hexagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	3.8.4.8
Schläfli symbol	t0,1(4,4,3)
Wythoff symbol	4 4 | 3
Coxeter diagram
Symmetry group	[(4,4,3)], (*443)
Dual	Order-4-4-3 t01 dual tiling
Properties	Vertex-transitive

In geometry, the cantic order-4 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t_0,1{(4,4,3)} or h₂{6,4}.

Uniform (4,4,3) tilings v t e
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)	h2{6,4} t0,1(4,4,3)	{4,6}1/2 t1(4,4,3)	h2{6,4} t1,2(4,4,3)	h{6,4} t2(4,4,3)	r{6,4}1/2 t0,2(4,4,3)	t{4,6}1/2 t0,1,2(4,4,3)	s{4,6}1/2 s(4,4,3)	hr{4,6}1/2 hr(4,3,4)	h{4,6}1/2 h(4,3,4)	q{4,6} h1(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

• 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.

Wikimedia Commons has media related to Uniform tiling 3-8-4-8.

• Hyperbolic space
• Square tiling
• Uniform tilings in hyperbolic plane
• List of regular polytopes

• 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 2n 33.n V33.n 42.n V42.n Regular 2∞ 36 44 63 Semi- regular 32.4.3.4 V32.4.3.4 33.42 33.∞ 34.6 V34.6 3.4.6.4 (3.6)2 3.122 42.∞ 4.6.12 4.82 Hyper- bolic 32.4.3.5 32.4.3.6 32.4.3.7 32.4.3.8 32.4.3.∞ 32.5.3.5 32.5.3.6 32.6.3.6 32.6.3.8 32.7.3.7 32.8.3.8 33.4.3.4 32.∞.3.∞ 34.7 34.8 34.∞ 35.4 37 38 3∞ (3.4)3 (3.4)4 3.4.62.4 3.4.7.4 3.4.8.4 3.4.∞.4 3.6.4.6 (3.7)2 (3.8)2 3.142 3.162 3.∞2 42.5.4 42.6.4 42.7.4 42.8.4 42.∞.4 45 46 47 48 4∞ (4.5)2 (4.6)2 4.6.12 4.6.14 V4.6.14 4.6.16 V4.6.16 4.6.∞ (4.7)2 (4.8)2 4.8.10 V4.8.10 4.8.12 4.8.14 4.8.16 4.8.∞ 4.102 4.10.12 4.122 4.12.16 4.142 4.162 4.∞2 54 55 56 5∞ 5.4.6.4 (5.6)2 5.82 5.102 5.122 64 65 66 68 6.4.8.4 (6.8)2 6.82 6.102 6.122 6.162 73 74 77 7.62 7.82 7.142 83 84 86 88 8.62 8.122 8.162 ∞3 ∞4 ∞5 ∞∞ ∞.62 ∞.82