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Contents

   



(Top)
 


1 Symmetry  





2 Related polyhedra and tilings  





3 See also  





4 References  





5 External links  














Rhombihexaoctagonal tiling







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From Wikipedia, the free encyclopedia
 


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
Wythoff symbol 6 | 8 2
Coxeter diagram
Symmetry group [8,6], (*862)
Dual Deltoidal hexaoctagonal tiling
Properties Vertex-transitive

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

Symmetry[edit]

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[edit]

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
  • 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[edit]

    References[edit]

    External links[edit]


    Retrieved from "https://en.wikipedia.org/w/index.php?title=Rhombihexaoctagonal_tiling&oldid=1189601934"

    Categories: 
    Hyperbolic tilings
    Isogonal tilings
    Semiregular tilings
    Hidden category: 
    Commons category link is on Wikidata
     



    This page was last edited on 12 December 2023, at 21:57 (UTC).

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