Cantic octagonal tiling

<h2 id="dual-tiling">Dual tiling</h2>

<h2 id="related-polyhedra-and-tiling">Related polyhedra and tiling</h2>
<a href="/facts/Uniform_tilings_in_hyperbolic_plane/khwIB6I1">Uniform (4,3,3) tilings</a><ul><li>v</li><li>t</li><li>e</li></ul><table> <tbody><tr><th colspan="7">Symmetry: [(4,3,3)], <a href="/facts/433_symmetry/5pEnULQ3">(*433)</a></th><th>[(4,3,3)]+, (433)</th></tr><tr><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th></tr><tr><th></th><th></th><th></th><th></th><th></th><th></th><th></th><th></th></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td><a href="/facts/Alternated_octagonal_tiling/xJkVW7LG">h{8,3}</a>t0(4,3,3)</td><td><a href="/facts/Trioctagonal_tiling/VlLfBMbl">r{3,8}1/2</a>t0,1(4,3,3)</td><td><a href="/facts/Alternated_octagonal_tiling/xJkVW7LG">h{8,3}</a>t1(4,3,3)</td><td>h2{8,3}t1,2(4,3,3)</td><td><a href="/facts/Order-8_triangular_tiling/feag8eNn">{3,8}1/2</a>t2(4,3,3)</td><td>h2{8,3}t0,2(4,3,3)</td><td><a href="/facts/Truncated_order-8_triangular_tiling/5pEnULQ3">t{3,8}1/2</a>t0,1,2(4,3,3)</td><td><a href="/facts/Snub_order-8_triangular_tiling/JrNvERlf">s{3,8}1/2</a>s(4,3,3)</td></tr><tr><th colspan="11">Uniform duals</th></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>V(3.4)3</td><td>V3.8.3.8</td><td>V(3.4)3</td><td>V3.6.4.6</td><td><a href="/facts/Octagonal_tiling/Fjj2z6ED">V(3.3)4</a></td><td>V3.6.4.6</td><td>V6.6.8</td><td>V3.3.3.3.3.4</td></tr></tbody></table>
*<i>n</i>33 orbifold symmetries of cantic tilings: <i>3.6.n.6</i><table><tbody><tr><th rowspan="2">Symmetry*n32[1+,2n,3]= [(n,3,3)]</th><th><a href="/facts/List_of_spherical_symmetry_groups/3X3YcHoQ">Spherical</a></th><th><a href="/facts/List_of_planar_symmetry_groups/3buKYIft">Euclidean</a></th><th colspan="3">Compact Hyperbolic</th><th>Paracompact</th></tr><tr><th>*233[1+,4,3]= [3,3]</th><th>*333[1+,6,3]= [(3,3,3)]</th><th>*433[1+,8,3]= [(4,3,3)]</th><th>*533[1+,10,3]= [(5,3,3)]</th><th>*633...[1+,12,3]= [(6,3,3)]</th><th>*∞33[1+,∞,3]= [(∞,3,3)]</th></tr><tr><th><a href="/facts/Coxeter%E2%80%93Dynkin_diagram/Ik6LmXJB">Coxeter</a><a href="/facts/Schl%C3%A4fli_symbol/jNQR77UU">Schläfli</a></th><th> = h2{4,3}</th><th> = h2{6,3}</th><th> = h2{8,3}</th><th> = h2{10,3}</th><th> = h2{12,3}</th><th> = h2{∞,3}</th></tr><tr><th>Canticfigure</th><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th><a href="/facts/Vertex_configuration/wWaBS6t0">Vertex</a></th><td><a href="/facts/Truncated_tetrahedron/K9ItvmUK">3.6.2.6</a></td><td><a href="/facts/Trihexagonal_tiling/spAKhDvd">3.6.3.6</a></td><td><a href="/facts/Tritetratrigonal_tiling/ESH3gujs">3.6.4.6</a></td><td>3.6.5.6</td><td>3.6.6.6</td><td>3.6.∞.6</td></tr><tr><th><a href="/facts/Fundamental_domain/e68KDYWu">Domain</a></th><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th><a href="/facts/Wythoff_construction/8yTYjp5e">Wythoff</a></th><td>2 3 | 3</td><td>3 3 | 3</td><td>4 3 | 3</td><td>5 3 | 3</td><td>6 3 | 3</td><td>∞ 3 | 3</td></tr><tr><th>Dualfigure</th><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><th><a href="/facts/Face_configuration/wWaBS6t0">Face</a></th><td><a href="/facts/Triakis_tetrahedron/qz6NNDMU">V3.6.2.6</a></td><td><a href="/facts/Rhombille_tiling/vKwFthpW">V3.6.3.6</a></td><td>V3.6.4.6</td><td>V3.6.5.6</td><td>V3.6.6.6</td><td>V3.6.∞.6</td></tr></tbody></table>
<h2 id="see-also">See also</h2>

Wikimedia Commons has media related to Uniform tiling 3-6-4-6.

<ul><li><a href="/facts/Square_tiling/3ym86mvv">Square tiling</a></li>
<li><a href="/facts/Uniform_tilings_in_hyperbolic_plane/khwIB6I1">Uniform tilings in hyperbolic plane</a></li>
<li><a href="/facts/List_of_regular_polytopes/Kng25Ymq">List of regular polytopes</a></li></ul>

<ul><li><a href="/facts/John_Horton_Conway/g3PA1zoK">John H. Conway</a>, Heidi Burgiel, Chaim Goodman-Strauss, <i>The Symmetries of Things</i> 2008, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)</li>
<li>"Chapter 10: Regular honeycombs in hyperbolic space". <i>The Beauty of Geometry: Twelve Essays</i>. Dover Publications. 1999. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-486-40919-8. <a href="/facts/LCCN_(identifier)/5hb5Cw2V">LCCN</a> <a href="https://lccn.loc.gov/99035678">99035678</a>.</li></ul>
<h2 id="external-links">External links</h2>
<ul><li><a href="/facts/Eric_W._Weisstein/FbMuVDep">Weisstein, Eric W.</a> <a href="https://mathworld.wolfram.com/HyperbolicTiling.html">"Hyperbolic tiling"</a>. <i><a href="/facts/MathWorld/yc1jodbq">MathWorld</a></i>.</li>
<li><a href="/facts/Eric_W._Weisstein/FbMuVDep">Weisstein, Eric W.</a> <a href="https://mathworld.wolfram.com/PoincareHyperbolicDisk.html">"Poincaré hyperbolic disk"</a>. <i><a href="/facts/MathWorld/yc1jodbq">MathWorld</a></i>.</li>
<li><a href="http://bork.hampshire.edu/~bernie/hyper/">Hyperbolic and Spherical Tiling Gallery</a> <a href="https://web.archive.org/web/20130324095520/http://bork.hampshire.edu/~bernie/hyper/">Archived</a> 2013-03-24 at the <a href="/facts/Wayback_Machine/nmQ3a6JC">Wayback Machine</a></li>
<li><a href="http://geometrygames.org/KaleidoTile/index.html">KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings</a></li>
<li><a href="http://www.plunk.org/~hatch/HyperbolicTesselations">Hyperbolic Planar Tessellations, Don Hatch</a></li></ul>

Cantic octagonal tiling open-in-new

Cantic octagonal tiling