Trioctagonal tiling

From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular octagonal tiling.

Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms.

Uniform octagonal/triangular tilings
Symmetry: [8,3], (*832)							[8,3]+ (832)	[1+,8,3] (*443)		[8,3+] (3*4)
{8,3}	t{8,3}	r{8,3}	t{3,8}	{3,8}	rr{8,3} s2{3,8}	tr{8,3}	sr{8,3}	h{8,3}	h2{8,3}	s{3,8}
								or	or
Uniform duals
V83	V3.16.16	V3.8.3.8	V6.6.8	V38	V3.4.8.4	V4.6.16	V34.8	V(3.4)3	V8.6.6	V35.4

It can also be generated from the (4 3 3) hyperbolic tilings:

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

The trioctagonal tiling can be seen in a sequence of quasiregular polyhedrons and tilings:

Quasiregular tilings: (3.n)2
Sym. *n32 [n,3]	Spherical			Euclid.	Compact hyperb.		Paraco.	Noncompact hyperbolic
	*332 [3,3] Td	*432 [4,3] Oh	*532 [5,3] Ih	*632 [6,3] p6m	*732 [7,3]	*832 [8,3]...	*∞32 [∞,3]	[12i,3]	[9i,3]	[6i,3]
Figure
Figure
Vertex	(3.3)2	(3.4)2	(3.5)2	(3.6)2	(3.7)2	(3.8)2	(3.∞)2	(3.12i)2	(3.9i)2	(3.6i)2
Schläfli	r{3,3}	r{3,4}	r{3,5}	r{3,6}	r{3,7}	r{3,8}	r{3,∞}	r{3,12i}	r{3,9i}	r{3,6i}
Coxeter
Dual uniform figures
Dual conf.	V(3.3)2	V(3.4)2	V(3.5)2	V(3.6)2	V(3.7)2	V(3.8)2	V(3.∞)2

Dimensional family of quasiregular polyhedra and tilings: (8.n)2
Symmetry *8n2 [n,8]	Hyperbolic...						Paracompact	Noncompact
	*832 [3,8]	*842 [4,8]	*852 [5,8]	*862 [6,8]	*872 [7,8]	*882 [8,8]...	*∞82 [∞,8]	[iπ/λ,8]
Coxeter
Quasiregular figures configuration	3.8.3.8	4.8.4.8	8.5.8.5	8.6.8.6	8.7.8.7	8.8.8.8	8.∞.8.∞	8.∞.8.∞

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

• Trihexagonal tiling - 3.6.3.6 tiling
  • Rhombille tiling - dual V3.6.3.6 tiling
• Tilings of regular polygons
• List of uniform tilings

• 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.

• Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
• Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch