Infinite-order pentagonal tiling

<h2 id="symmetry">Symmetry</h2>
<p>There is a half symmetry form, , seen with alternating colors:
</p>

<h2 id="related-polyhedra-and-tiling">Related polyhedra and tiling</h2>
<p>This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (5n).
</p>
<table><tbody><tr><th>Finite</th><th colspan="5">Compact hyperbolic <ul><li>v</li><li>t</li><li>e</li></ul></th><th>Paracompact</th></tr><tr><td><a href="/facts/Dodecahedron/7r519eCl">{5,3}</a></td><td><a href="/facts/Order-4_pentagonal_tiling/aHah4SUB">{5,4}</a></td><td><a href="/facts/Order-5_pentagonal_tiling/8oTt2xQ1">{5,5}</a></td><td><a href="/facts/Order-6_pentagonal_tiling/BUwKYQ77">{5,6}</a></td><td><a href="/facts/Order-7_pentagonal_tiling/Kng25Ymq">{5,7}</a></td><td><a href="/facts/Order-8_pentagonal_tiling/MTB6bW1G">{5,8}</a>...</td><td>{5,∞}</td></tr></tbody></table>
<table><tbody><tr><th colspan="12">Paracompact uniform apeirogonal/pentagonal tilings <ul><li>v</li><li>t</li><li>e</li></ul></th></tr><tr><th colspan="7">Symmetry: [∞,5], (*∞52)</th><th>[∞,5]+(∞52)</th><th colspan="2">[1+,∞,5](*∞55)</th><th>[∞,5+](5*∞)</th></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td><a href="/facts/Order-5_apeirogonal_tiling/wF0evtKd">{∞,5}</a></td><td>t{∞,5}</td><td>r{∞,5}</td><td>2t{∞,5}=t{5,∞}</td><td>2r{∞,5}={5,∞}</td><td>rr{∞,5}</td><td>tr{∞,5}</td><td>sr{∞,5}</td><td>h{∞,5}</td><td>h2{∞,5}</td><td>s{5,∞}</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><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>V∞5</td><td>V5.∞.∞</td><td>V5.∞.5.∞</td><td>V∞.10.10</td><td>V5∞</td><td>V4.5.4.∞</td><td>V4.10.∞</td><td>V3.3.5.3.∞</td><td></td><td>V(∞.5)5</td><td>V3.5.3.5.3.∞</td></tr></tbody></table>
<h2 id="see-also">See also</h2>

Wikimedia Commons has media related to Infinite-order pentagonal tiling.

<ul><li><a href="/facts/Pentagonal_tiling/zAEA5rzw">Pentagonal 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 (2008). "Chapter 19, The Hyperbolic Archimedean Tessellations". <i>The Symmetries of Things</i>. Taylor & Francis. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1-56881-220-5.</li>
<li><a href="/facts/Harold_Scott_MacDonald_Coxeter/D2l5jWGG">H. S. M. Coxeter</a> (1999). "Chapter 10: Regular honeycombs in hyperbolic space". <i>The Beauty of Geometry: Twelve Essays</i>. Dover Publications. <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></ul>

Infinite-order pentagonal tiling open-in-new

Infinite-order pentagonal tiling