https://en.formulasearchengine.com/w/api.php?action=feedcontributions&feedformat=atom&user=18.41.1.218 formulasearchengine - User contributions [en] 2026-08-24T23:01:16Z User contributions MediaWiki 1.47.0-wmf.7 https://en.formulasearchengine.com/w/index.php?title=Conformal_loop_ensemble&diff=27950 Conformal loop ensemble 2013-10-02T18:31:07Z <p>18.41.1.218: /* Properties */</p> <hr /> <div>{| class=&quot;wikitable&quot;<br /> |+ <br /> [[Uniform_1_k2_polytope|1&lt;sub&gt;k2&lt;/sub&gt; figures]] in ''n'' dimensions<br /> |-<br /> !''n'' <br /> ![[Three-dimensional space|4]]<br /> ![[Four-dimensional space|4]]<br /> ![[Five-dimensional space|5]]<br /> ![[Six-dimensional space|6]]<br /> ![[Seven-dimensional space|7]]<br /> ![[Eight-dimensional space|8]]<br /> ![[Nine-dimensional space|9]]<br /> ![[Ten-dimensional space|10]]<br /> |- align=center<br /> ![[Coxeter group|Coxeter&lt;BR&gt;group]]<br /> |E&lt;sub&gt;3&lt;/sub&gt;=A&lt;sub&gt;2&lt;/sub&gt;×A&lt;sub&gt;1&lt;/sub&gt;<br /> |E&lt;sub&gt;4&lt;/sub&gt;=A&lt;sub&gt;4&lt;/sub&gt;<br /> |E&lt;sub&gt;5&lt;/sub&gt;=D&lt;sub&gt;5&lt;/sub&gt;<br /> |[[E6 (mathematics)|E&lt;sub&gt;6&lt;/sub&gt;]]<br /> |[[E7 (mathematics)|E&lt;sub&gt;7&lt;/sub&gt;]]<br /> |[[E8 (mathematics)|E&lt;sub&gt;8&lt;/sub&gt;]]<br /> |E&lt;sub&gt;9&lt;/sub&gt; = &lt;math&gt;{\tilde{E}}_{8}&lt;/math&gt; = E&lt;sub&gt;8&lt;/sub&gt;&lt;sup&gt;+&lt;/sup&gt;<br /> |E&lt;sub&gt;10&lt;/sub&gt; = E&lt;sub&gt;8&lt;/sub&gt;&lt;sup&gt;++&lt;/sup&gt;<br /> |- align=center<br /> ![[Coxeter-Dynkin diagram|Coxeter&lt;BR&gt;diagram]]<br /> |{{CDD|node|3|node|2|node_1}}<br /> |{{CDD|nodea|3a|nodea|3a|branch_01l}}<br /> |{{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea}}<br /> |{{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea}}<br /> |{{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea}}<br /> |{{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}<br /> |{{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}<br /> |{{CDD|nodea|3a|nodea|3a|branch_01lr|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea|3a|nodea}}<br /> |- align=center<br /> ![[Coxeter notation|Symmetry]]&lt;BR&gt;(order)<br /> |[3&lt;sup&gt;-1,2,1&lt;/sup&gt;]&lt;BR&gt;(12)<br /> |[3&lt;sup&gt;0,2,1&lt;/sup&gt;]&lt;BR&gt;(120)<br /> |[3&lt;sup&gt;1,2,1&lt;/sup&gt;]&lt;BR&gt;(192)<br /> |[[3&lt;sup&gt;2,2,1&lt;/sup&gt;]]&lt;BR&gt;(103,680)<br /> |[3&lt;sup&gt;3,2,1&lt;/sup&gt;]&lt;BR&gt;(2,903,040)<br /> |[3&lt;sup&gt;4,2,1&lt;/sup&gt;]&lt;BR&gt;(696,729,600)<br /> |[3&lt;sup&gt;5,2,1&lt;/sup&gt;]&lt;BR&gt;(&amp;infin;)<br /> |[3&lt;sup&gt;6,2,1&lt;/sup&gt;]&lt;BR&gt;(&amp;infin;)<br /> |- align=center<br /> !Graph<br /> |[[File:Trigonal hosohedron.png|80px]]<br /> |[[File:4-simplex t0.svg|80px]]<br /> |[[File:Demipenteract graph ortho.svg|80px]]<br /> |[[File:Up_1_22_t0_E6.svg|80px]]<br /> |[[File:Up2_1_32_t0_E7.svg|80px]]<br /> |[[File:Gosset_1_42_polytope_petrie.svg|80px]]<br /> |&amp;infin;<br /> |&amp;infin;<br /> |- align=center<br /> !Name<br /> |[[Hosohedron|1&lt;sub&gt;-1,2&lt;/sup&gt;]]<br /> |[[5-cell|1&lt;sub&gt;02&lt;/sup&gt;]]<br /> |[[Demipenteract|1&lt;sub&gt;12&lt;/sup&gt;]]<br /> |[[1 22 polytope|1&lt;sub&gt;22&lt;/sup&gt;]]<br /> |[[1 32 polytope|1&lt;sub&gt;32&lt;/sup&gt;]]<br /> |[[1 42 polytope|1&lt;sub&gt;42&lt;/sup&gt;]]<br /> |[[1 52 honeycomb|1&lt;sub&gt;52&lt;/sup&gt;]]<br /> |[[1 62 honeycomb|1&lt;sub&gt;62&lt;/sup&gt;]]<br /> |}&lt;noinclude&gt;[[Category:Encyclopedic content templates]]&lt;/noinclude&gt;</div> 18.41.1.218