Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Infinite-order hexagonal tiling
open-in-new
<table><tbody><tr><th colspan="2">Infinite-order hexagonal tiling</th></tr><tr><td colspan="2"><a href="/facts/Poincar%C3%A9_disk_model/6nCWjbRL">Poincaré disk model</a> of the <a href="/facts/Hyperbolic_geometry/DjTMKdgy">hyperbolic plane</a></td></tr><tr><td>Type</td><td><a href="/facts/List_of_regular_polytopes/Kng25Ymq">Hyperbolic regular tiling</a></td></tr><tr><td><a href="/facts/Vertex_configuration/wWaBS6t0">Vertex configuration</a></td><td>6∞</td></tr><tr><td><a href="/facts/Schl%C3%A4fli_symbol/jNQR77UU">Schläfli symbol</a></td><td>{6,∞}</td></tr><tr><td><a href="/facts/Wythoff_symbol/ECD0Wl5x">Wythoff symbol</a></td><td>∞ | 6 2</td></tr><tr><td><a href="/facts/Coxeter%E2%80%93Dynkin_diagram/Ik6LmXJB">Coxeter diagram</a></td><td></td></tr><tr><td><a href="/facts/Coxeter%E2%80%93Dynkin_diagram/Ik6LmXJB">Symmetry group</a></td><td>[∞,6], (*∞62)</td></tr><tr><td><a href="/facts/Dual_polyhedron/rkIHbmAf">Dual</a></td><td><a href="/facts/Order-6_apeirogonal_tiling/3jXwGWfp">Order-6 apeirogonal tiling</a></td></tr><tr><td>Properties</td><td><a href="/facts/Vertex-transitive/5nC8PdBm">Vertex-transitive</a>, <a href="/facts/Edge-transitive/p5j7GhwX">edge-transitive</a>, <a href="/facts/Face-transitive/ukLVQlK2">face-transitive</a></td></tr></tbody></table> <p>In 2-dimensional <a href="/facts/Hyperbolic_geometry/DjTMKdgy">hyperbolic geometry</a>, the infinite-order hexagonal tiling is a <a href="/facts/List_of_regular_polytopes/Kng25Ymq">regular</a> tiling. It has <a href="/facts/Schl%C3%A4fli_symbol/jNQR77UU">Schläfli symbol</a> of {6,∞}. All vertices are <i>ideal</i>, located at "infinity", seen on the boundary of the <a href="/facts/Poincar%C3%A9_hyperbolic_disk/4mg3Mj2b">Poincaré hyperbolic disk</a> projection. </p>