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Cosmochoron - Revision history
2024-03-28T16:30:33Z
Revision history for this page on the wiki
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Username5243: /* Coordinates */
2017-03-26T14:34:38Z
<p><span class="autocomment">Coordinates</span></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 14:34, 26 March 2017</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The coordinates of the 120-cell with edge length 2/φ<sup>2</sup> are all permutations of coordinates and changes of sign of:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The coordinates of the 120-cell with edge length 2/φ<sup>2</sup> are all permutations of coordinates and changes of sign of:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>(2, 2, 0, 0)</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>(2, 2, 0, 0)<ins class="diffchange diffchange-inline"><br></ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>(√5, 1, 1, 1)</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>(√5, 1, 1, 1)<ins class="diffchange diffchange-inline"><br></ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>(φ, φ, φ, 2-φ)</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>(φ, φ, φ, 2-φ)<ins class="diffchange diffchange-inline"><br></ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>(φ+1, φ−1, φ−1, φ−1)</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>(φ+1, φ−1, φ−1, φ−1)<ins class="diffchange diffchange-inline"><br></ins></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">together </del>with all even permutations of coordinates and all changes of sign of:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">Together </ins>with all even permutations of coordinates and all changes of sign of:</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">(φ+1, 2-φ, 1, 0)<br></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">(√5, φ−1, φ, 0)<br></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">(2, 1, φ, φ−1)<br></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">(φ+1, 2-φ, 1, 0)</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">(√5, φ−1, φ, 0)</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">(2, 1, φ, φ−1)</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Equations ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Equations ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*The [[hypervolume]]s of a cosmochoron with side length ''l'' are given by:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*The [[hypervolume]]s of a cosmochoron with side length ''l'' are given by:</div></td></tr>
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Username5243
http://hi.gher.space/w/index.php?title=Cosmochoron&diff=8940&oldid=prev
Username5243 at 14:32, 26 March 2017
2017-03-26T14:32:47Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 14:32, 26 March 2017</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Each dodecahedron in its [[net]] lies on a ring of ten dodecahedra along a [[great circle]] of the [[glome]]. There are four dodecahedra on such a ring between any dodecahedron and its antipodal dodecahedron.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Each dodecahedron in its [[net]] lies on a ring of ten dodecahedra along a [[great circle]] of the [[glome]]. There are four dodecahedra on such a ring between any dodecahedron and its antipodal dodecahedron.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==Coordinates==</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">The coordinates of the 120-cell with edge length 2/φ<sup>2</sup> are all permutations of coordinates and changes of sign of:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">(2, 2, 0, 0)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">(√5, 1, 1, 1)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">(φ, φ, φ, 2-φ)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">(φ+1, φ−1, φ−1, φ−1)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">together with all even permutations of coordinates and all changes of sign of:</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">(φ+1, 2-φ, 1, 0)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">(√5, φ−1, φ, 0)</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">(2, 1, φ, φ−1)</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Equations ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Equations ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*The [[hypervolume]]s of a cosmochoron with side length ''l'' are given by:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*The [[hypervolume]]s of a cosmochoron with side length ''l'' are given by:</div></td></tr>
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Username5243
http://hi.gher.space/w/index.php?title=Cosmochoron&diff=8912&oldid=prev
Username5243 at 02:17, 26 March 2017
2017-03-26T02:17:59Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 02:17, 26 March 2017</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{STS Shape</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{STS Shape</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| dim=4</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| dim=4</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>| elements=120, 720, 1200, 600</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>| elements=120 <ins class="diffchange diffchange-inline">[[Dodecahedron|dodecahedra]]</ins>, 720 <ins class="diffchange diffchange-inline">[[pentagon]]s</ins>, 1200 <ins class="diffchange diffchange-inline">[[digon]]s</ins>, 600 <ins class="diffchange diffchange-inline">[[point]]s</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| genus=0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| genus=0</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc=<nowiki>{{</nowiki>G5<sup>3</sup>}<sup>4</sup>}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc=<nowiki>{{</nowiki>G5<sup>3</sup>}<sup>4</sup>}</div></td></tr>
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Username5243
http://hi.gher.space/w/index.php?title=Cosmochoron&diff=8910&oldid=prev
Username5243 at 02:10, 26 March 2017
2017-03-26T02:10:32Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 02:10, 26 March 2017</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc2=Ks1</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc2=Ks1</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| extra={{STS Polytope</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| extra={{STS Polytope</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">| symbol=x5o3o3o</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| flayout={{FLD|dim=4|left=e3|erev|a5|end2|e3}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| flayout={{FLD|dim=4|left=e3|erev|a5|end2|e3}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| petrie=30, 60, 30, 60,<br>60, 60, 60, 60,<br>60, 30, 60, 30, 0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| petrie=30, 60, 30, 60,<br>60, 60, 60, 60,<br>60, 30, 60, 30, 0</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}{{STS Uniform polytope</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}{{STS Uniform polytope</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| schlaefli={[[Pentagon|5,]][[Dodecahedron|3,]]3}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| schlaefli={[[Pentagon|5,]][[Dodecahedron|3,]]3}</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">| dynkin=x5o3o3o</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vlayout=([[Pentagon|5]][[Dodecahedron|<sup>3</sup>]])<sup>4</sup></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vlayout=([[Pentagon|5]][[Dodecahedron|<sup>3</sup>]])<sup>4</sup></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vfigure=[[Tetrahedron]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vfigure=[[Tetrahedron]]</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>total surface area = 180√(25 + 10√5) {{DotHV}}<br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>total surface area = 180√(25 + 10√5) {{DotHV}}<br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>surcell volume = 30(15 + 7√5) {{DotHV|3}}<br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>surcell volume = 30(15 + 7√5) {{DotHV|3}}<br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>bulk = <del class="diffchange diffchange-inline">''Unknown''</del></blockquote></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>bulk = <ins class="diffchange diffchange-inline">{{Over|15|4}}(105 + 47√5) {{DotHV|4}}</ins></blockquote></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Projection ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Projection ==</div></td></tr>
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Username5243
http://hi.gher.space/w/index.php?title=Cosmochoron&diff=8777&oldid=prev
Hayate: add symbol
2016-03-13T11:43:13Z
<p>add symbol</p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 11:43, 13 March 2016</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc2=Ks1</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc2=Ks1</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| extra={{STS Polytope</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| extra={{STS Polytope</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">| symbol=x5o3o3o</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| flayout={{FLD|dim=4|left=e3|erev|a5|end2|e3}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| flayout={{FLD|dim=4|left=e3|erev|a5|end2|e3}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| petrie=30, 60, 30, 60,<br>60, 60, 60, 60,<br>60, 30, 60, 30, 0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| petrie=30, 60, 30, 60,<br>60, 60, 60, 60,<br>60, 30, 60, 30, 0</div></td></tr>
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Hayate
http://hi.gher.space/w/index.php?title=Cosmochoron&diff=8123&oldid=prev
Hayate: move Bowers acronym from Template:STS Uniform polytope as it is now being used for non-uniforms too
2014-03-02T09:29:30Z
<p>move Bowers acronym from <a href="/wiki/Template:STS_Uniform_polytope" title="Template:STS Uniform polytope (Meta, no ontology)" class="kind-meta">Template:STS Uniform polytope</a> as it is now being used for non-uniforms too</p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 09:29, 2 March 2014</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| petrie=30, 60, 30, 60,<br>60, 60, 60, 60,<br>60, 30, 60, 30, 0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| petrie=30, 60, 30, 60,<br>60, 60, 60, 60,<br>60, 30, 60, 30, 0</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| dual=[[Hydrochoron]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| dual=[[Hydrochoron]]</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">| bowers=Hi</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}{{STS Uniform polytope</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}{{STS Uniform polytope</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| schlaefli={[[Pentagon|5,]][[Dodecahedron|3,]]3}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| schlaefli={[[Pentagon|5,]][[Dodecahedron|3,]]3}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vlayout=([[Pentagon|5]][[Dodecahedron|<sup>3</sup>]])<sup>4</sup></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vlayout=([[Pentagon|5]][[Dodecahedron|<sup>3</sup>]])<sup>4</sup></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vfigure=[[Tetrahedron]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vfigure=[[Tetrahedron]]</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">| bowers=Hi</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The '''cosmochoron''', also known as the '''hecatonicosachoron''' and the '''120-cell''', is a 4D polytope bounded by 120 [[dodecahedra]]. It is the highest dimensional analog of the [[pentagon]] and the dodecahedron.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The '''cosmochoron''', also known as the '''hecatonicosachoron''' and the '''120-cell''', is a 4D polytope bounded by 120 [[dodecahedra]]. It is the highest dimensional analog of the [[pentagon]] and the dodecahedron.</div></td></tr>
</table>
Hayate
http://hi.gher.space/w/index.php?title=Cosmochoron&diff=7827&oldid=prev
Hayate: polytope explorer integration
2014-02-16T21:27:38Z
<p>polytope explorer integration</p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 21:27, 16 February 2014</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Note that only the projection is rotating; the 4D shape itself is not.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Note that only the projection is rotating; the 4D shape itself is not.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><<del class="diffchange diffchange-inline">br clear="all"><br</del>></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><<ins class="diffchange diffchange-inline">[#polytope [id 40]]</ins>></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Tetrashapes}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Tetrashapes}}</div></td></tr>
</table>
Hayate
http://hi.gher.space/w/index.php?title=Cosmochoron&diff=7610&oldid=prev
Hayate: K6.4 upgrade: img -> embed
2014-02-11T19:44:28Z
<p>K6.4 upgrade: img -> embed</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Projection ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Projection ==</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><[#<del class="diffchange diffchange-inline">img </del>[hash XN0PP2G3K4HZT6489B2ZYT8D15]]> <[#<del class="diffchange diffchange-inline">img </del>[hash NK06P7XH2G01YTY3EYK0T5BGDQ]]></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><[#<ins class="diffchange diffchange-inline">embed </ins>[hash XN0PP2G3K4HZT6489B2ZYT8D15]]> <[#<ins class="diffchange diffchange-inline">embed </ins>[hash NK06P7XH2G01YTY3EYK0T5BGDQ]]></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Here are two perspective projections of the hecatonicosachoron into 3D. The highlighted center cell is closest to the 4D viewpoint. It is surrounded by 12 [[dodecahedra]] in a second layer. The right-hand image also shows the third layer of 32 dodecahedra. After this is a fourth layer of 30 dodecahedra lying on the spherical "equator", followed by three more layers mirroring the three layers seen here (not seen here, because they lie on the 4D "back" of the shape).</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Here are two perspective projections of the hecatonicosachoron into 3D. The highlighted center cell is closest to the 4D viewpoint. It is surrounded by 12 [[dodecahedra]] in a second layer. The right-hand image also shows the third layer of 32 dodecahedra. After this is a fourth layer of 30 dodecahedra lying on the spherical "equator", followed by three more layers mirroring the three layers seen here (not seen here, because they lie on the 4D "back" of the shape).</div></td></tr>
</table>
Hayate
http://hi.gher.space/w/index.php?title=Cosmochoron&diff=6594&oldid=prev
Hayate: fix equations
2011-11-18T01:11:11Z
<p>fix equations</p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 01:11, 18 November 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*The [[hypervolume]]s of a cosmochoron with side length ''l'' are given by:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*The [[hypervolume]]s of a cosmochoron with side length ''l'' are given by:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><blockquote>total edge length = 1200''l''<br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><blockquote>total edge length = 1200''l''<br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>total surface area = <del class="diffchange diffchange-inline">180''l''<sup>2</sup>sqrt</del>(25+<del class="diffchange diffchange-inline">10sqrt(5)</del>)<br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>total surface area = <ins class="diffchange diffchange-inline">180√</ins>(25 + <ins class="diffchange diffchange-inline">10√5</ins>) <ins class="diffchange diffchange-inline">{{DotHV}}</ins><br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>surcell volume = <del class="diffchange diffchange-inline">300''l''<sup>3</sup></del>(<del class="diffchange diffchange-inline">tan(3π10<sup>-1</sup>))<sup>2</sup>(tan(sin<sup>-1</sup>(2sin(π5<sup>-1</sup>))<sup>-1</sup>)</del>)<br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>surcell volume = <ins class="diffchange diffchange-inline">30</ins>(<ins class="diffchange diffchange-inline">15 + 7√5</ins>) <ins class="diffchange diffchange-inline">{{DotHV|3}}</ins><br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>bulk = ''Unknown''</blockquote></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>bulk = ''Unknown''</blockquote></div></td></tr>
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Hayate
http://hi.gher.space/w/index.php?title=Cosmochoron&diff=6509&oldid=prev
Hayate at 20:32, 12 March 2011
2011-03-12T20:32:38Z
<p></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 20:32, 12 March 2011</td>
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<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"><[#ontology [kind topic] [cats 4D Regular Polytope]]></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{STS Shape</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{STS Shape</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| dim=4</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| dim=4</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| flayout={{FLD|dim=4|left=e3|erev|a5|end2|e3}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| flayout={{FLD|dim=4|left=e3|erev|a5|end2|e3}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| petrie=30, 60, 30, 60,<br>60, 60, 60, 60,<br>60, 30, 60, 30, 0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| petrie=30, 60, 30, 60,<br>60, 60, 60, 60,<br>60, 30, 60, 30, 0</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>| dual=[[<del class="diffchange diffchange-inline">サコ</del>]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>| dual=[[<ins class="diffchange diffchange-inline">Hydrochoron</ins>]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}{{STS Uniform polytope</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}{{STS Uniform polytope</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| schlaefli={[[Pentagon|5,]][[Dodecahedron|3,]]3}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| schlaefli={[[Pentagon|5,]][[Dodecahedron|3,]]3}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vlayout=([[Pentagon|5]][[Dodecahedron|<sup>3</sup>]])<sup>4</sup></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vlayout=([[Pentagon|5]][[Dodecahedron|<sup>3</sup>]])<sup>4</sup></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>| vfigure=[[<del class="diffchange diffchange-inline">テ</del>]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>| vfigure=[[<ins class="diffchange diffchange-inline">Tetrahedron</ins>]]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| bowers=Hi</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| bowers=Hi</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">| kana=ヘカ</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The '''cosmochoron''', also known as the '''hecatonicosachoron''' and the '''120-cell''', is a 4D polytope bounded by 120 [[dodecahedra]]. It is the highest dimensional analog of the [[pentagon]] and the dodecahedron.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The '''cosmochoron''', also known as the '''hecatonicosachoron''' and the '''120-cell''', is a 4D polytope bounded by 120 [[dodecahedra]]. It is the highest dimensional analog of the [[pentagon]] and the dodecahedron.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Tetrashapes}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Tetrashapes}}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">[[Category:Regular polychora]]</del></div></td><td colspan="2"> </td></tr>
</table>
Hayate