Alternated order-4 hexagonal tiling

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Alternated order-4 hexagonal tiling
Alternated order-4 hexagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration (3.4)4
Schläfli symbol h{6,4} or (3,4,4)
Wythoff symbol 4 | 3 4
Coxeter diagram CDel branch 01rd.pngCDel split2-44.pngCDel node.png or CDel node h1.pngCDel 6.pngCDel node.pngCDel 4.pngCDel node.png
Symmetry group [(4,4,3)], (*443)
Dual Order-4-4-3_t0 dual tiling
Properties Vertex-transitive

In geometry, the alternated order-4 hexagonal tiling or ditetragonal tritetratrigonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of (3,4,4), h{6,4}, and hr{6,6}.

Uniform constructions[edit]

There are four uniform constructions, with some of lower ones which can be seen with two colors of triangles:

*443 3333 *3232 3*22
CDel node h1.pngCDel 6.pngCDel node.pngCDel 4.pngCDel node.png = CDel branch 10ru.pngCDel split2-44.pngCDel node.png CDel node h.pngCDel 6.pngCDel node g.pngCDel 4sg.pngCDel node g.png = CDel branch hh.pngCDel 3a3b-cross.pngCDel branch hh.png CDel node h1.pngCDel 6.pngCDel node.pngCDel 4.pngCDel node h0.png = CDel node h1.pngCDel split1-66.pngCDel nodes.png = CDel nodes 11.pngCDel 3a3b-cross.pngCDel nodes.png CDel node h.pngCDel 6.pngCDel node h0.pngCDel 4.pngCDel node.png = CDel branch hh.pngCDel 2a2b-cross.pngCDel nodes.png
H2 tiling 344-1.png Uniform tiling verf 34343434.png
(4,4,3) = h{6,4} hr{6,6} = h{6,4}​12

Related polyhedra and tiling[edit]

References[edit]

  • 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.

See also[edit]

External links[edit]