[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/tetrahexagonal-tiling-wikipedia\/#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/en\/wiki24\/tetrahexagonal-tiling-wikipedia\/","headline":"Tetrahexagonal tiling – Wikipedia","name":"Tetrahexagonal tiling – Wikipedia","description":"before-content-x4 From Wikipedia, the free encyclopedia Tetrahexagonal tiling Poincar\u00e9 disk model of the hyperbolic plane Type Hyperbolic uniform tiling Vertex","datePublished":"2014-12-09","dateModified":"2014-12-09","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/author\/lordneo\/#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/en\/wiki24\/author\/lordneo\/","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/3\/3c\/H2_tiling_246-2.png\/280px-H2_tiling_246-2.png","url":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/3\/3c\/H2_tiling_246-2.png\/280px-H2_tiling_246-2.png","height":"280","width":"280"},"url":"https:\/\/wiki.edu.vn\/en\/wiki24\/tetrahexagonal-tiling-wikipedia\/","about":["Wiki"],"wordCount":18649,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4From Wikipedia, the free encyclopediaTetrahexagonal tilingPoincar\u00e9 disk model of the hyperbolic planeTypeHyperbolic uniform tilingVertex configuration(4.6)2Schl\u00e4fli symbolr{6,4} or {64}{displaystyle {begin{Bmatrix}6\\4end{Bmatrix}}}       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4rr{6,6}r(4,4,3)t0,1,2,3(\u221e,3,\u221e,3)Wythoff symbol2 | 6 4Coxeter diagram or  or Symmetry group[6,4], (*642)[6,6], (*662)[(4,4,3)], (*443)[(\u221e,3,\u221e,3)], (*3232)DualOrder-6-4 quasiregular rhombic tilingPropertiesVertex-transitive edge-transitiveIn geometry, the tetrahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schl\u00e4fli symbol r{6,4}.       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Table of ContentsConstructions[edit]Symmetry[edit]Related polyhedra and tiling[edit]See also[edit]References[edit]External links[edit]Constructions[edit]There are for uniform constructions of this tiling, three of them as constructed by mirror removal from the [6,4] kaleidoscope. Removing the last mirror, [6,4,1+], gives [6,6], (*662). Removing the first mirror [1+,6,4], gives [(4,4,3)], (*443). Removing both mirror as [1+,6,4,1+], leaving [(3,\u221e,3,\u221e)] (*3232).Four uniform constructions of 4.6.4.6UniformColoringFundamentalDomainsSchl\u00e4flir{6,4}r{4,6}1\u20442r{6,4}1\u20442r{6,4}1\u20444Symmetry[6,4](*642)[6,6] = [6,4,1+](*662)[(4,4,3)] = [1+,6,4](*443)[(\u221e,3,\u221e,3)] = [1+,6,4,1+](*3232) or Symbolr{6,4}rr{6,6}r(4,3,4)t0,1,2,3(\u221e,3,\u221e,3)Coxeterdiagram =  =  = or Symmetry[edit]The dual tiling, called a rhombic tetrahexagonal tiling, with face configuration V4.6.4.6, and represents the fundamental domains of a quadrilateral kaleidoscope, orbifold (*3232), shown here in two different centered views. Adding a 2-fold rotation point in the center of each rhombi represents a (2*32) orbifold.       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4Related polyhedra and tiling[edit]Uniform tetrahexagonal tilings Symmetry: [6,4], (*642)(with [6,6] (*662), [(4,3,3)] (*443) , [\u221e,3,\u221e] (*3222) index 2 subsymmetries)(And [(\u221e,3,\u221e,3)] (*3232) index 4 subsymmetry)= = = = = = = = = = = = {6,4}t{6,4}r{6,4}t{4,6}{4,6}rr{6,4}tr{6,4}Uniform dualsV64V4.12.12V(4.6)2V6.8.8V46V4.4.4.6V4.8.12Alternations[1+,6,4](*443)[6+,4](6*2)[6,1+,4](*3222)[6,4+](4*3)[6,4,1+](*662)[(6,4,2+)](2*32)[6,4]+(642)= = = = = = h{6,4}s{6,4}hr{6,4}s{4,6}h{4,6}hrr{6,4}sr{6,4}Uniform hexahexagonal tilings Symmetry: [6,6], (*662) = =  = =  = =  = =  = =  = =   == {6,6}= h{4,6}t{6,6}= h2{4,6}r{6,6}{6,4}t{6,6}= h2{4,6}{6,6}= h{4,6}rr{6,6}r{6,4}tr{6,6}t{6,4}Uniform dualsV66V6.12.12V6.6.6.6V6.12.12V66V4.6.4.6V4.12.12Alternations[1+,6,6](*663)[6+,6](6*3)[6,1+,6](*3232)[6,6+](6*3)[6,6,1+](*663)[(6,6,2+)](2*33)[6,6]+(662) =  =  = h{6,6}s{6,6}hr{6,6}s{6,6}h{6,6}hrr{6,6}sr{6,6}Uniform (4,4,3) tilings Symmetry: [(4,4,3)] (*443)[(4,4,3)]+(443)[(4,4,3+)](3*22)[(4,1+,4,3)](*3232)h{6,4}t0(4,4,3)h2{6,4}t0,1(4,4,3){4,6}1\/2t1(4,4,3)h2{6,4}t1,2(4,4,3)h{6,4}t2(4,4,3)r{6,4}1\/2t0,2(4,4,3)t{4,6}1\/2t0,1,2(4,4,3)s{4,6}1\/2s(4,4,3)hr{4,6}1\/2hr(4,3,4)h{4,6}1\/2h(4,3,4)q{4,6}h1(4,3,4)Uniform dualsV(3.4)4V3.8.4.8V(4.4)3V3.8.4.8V(3.4)4V4.6.4.6V6.8.8V3.3.3.4.3.4V(4.4.3)2V66V4.3.4.6.6See also[edit]References[edit]External links[edit]       (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/en\/wiki24\/tetrahexagonal-tiling-wikipedia\/#breadcrumbitem","name":"Tetrahexagonal tiling – Wikipedia"}}]}]