Rhombihexaoctagonal tiling

Rhombihexaoctagonal tiling
Poincaré disk model of the hyperbolic plane
Type	Hyperbolic uniform tiling
Vertex configuration	6.4.8.4
Schläfli symbol	rr{8,6} or ${\displaystyle r{\begin{Bmatrix}8\\6\end{Bmatrix}}}$
Wythoff symbol	6 | 8 2
Coxeter diagram
Symmetry group	[8,6], (*862)
Dual	Deltoidal hexaoctagonal tiling
Properties	Vertex-transitive

In geometry, the rhombihexaoctagonal tiling is a semiregular tiling of the hyperbolic plane. It has Schläfli symbol of rr{8,6}.

Symmetry

The dual tiling, called a deltoidal hexaoctagonal tiling represent the fundamental domains of *4232 symmetry, a half symmetry of [8,6], (*862) as [8,1⁺,6].

Related polyhedra and tilings

From a Wythoff construction there are fourteen hyperbolic uniform tilings that can be based from the regular order-6 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 7 forms with full [8,6] symmetry, and 7 with subsymmetry.

Uniform octagonal/hexagonal tilings v t e
Symmetry: [8,6], (*862)
{8,6}	t{8,6}	r{8,6}	2t{8,6}=t{6,8}	2r{8,6}={6,8}	rr{8,6}	tr{8,6}
Uniform duals
V86	V6.16.16	V(6.8)2	V8.12.12	V68	V4.6.4.8	V4.12.16
Alternations
[1+,8,6] (*466)	[8+,6] (8*3)	[8,1+,6] (*4232)	[8,6+] (6*4)	[8,6,1+] (*883)	[(8,6,2+)] (2*43)	[8,6]+ (862)
h{8,6}	s{8,6}	hr{8,6}	s{6,8}	h{6,8}	hrr{8,6}	sr{8,6}
Alternation duals
V(4.6)6	V3.3.8.3.8.3	V(3.4.4.4)2	V3.4.3.4.3.6	V(3.8)8	V3.45	V3.3.6.3.8

See also

Wikimedia Commons has media related to Uniform tiling 4-6-4-8.