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Alternated order-4 hexagonal tiling

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}.

Contents

Uniform constructionsEdit

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

*443 3333 *3232 3*22
      =           =           =     =           =    
   
(4,4,3) = h{6,4} hr{6,6} = h{6,4}​12

Related polyhedra and tilingEdit

ReferencesEdit

  • 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 alsoEdit

External linksEdit