http://hi.gher.space/w/index.php?title=Pyrochoron&feed=atom&action=historyPyrochoron - Revision history2024-03-28T17:36:43ZRevision history for this page on the wikiMediaWiki 1.16.2http://hi.gher.space/w/index.php?title=Pyrochoron&diff=8934&oldid=prevUsername5243 at 14:08, 26 March 20172017-03-26T14:08:15Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The '''pyrochoron''', also known as the '''pentachoron''' and the '''5-cell''', is the four-dimensional [[simplex]], and has the lowest possible element count of any [[flat]], non-[[degenerate]] four-dimensional shape. It consists of 5 regular tetrahedra joined at their faces, folded into 4D to form a 4D volume. It is a special case of the [[pyramid]] where the base is a [[tetrahedron]]. There are 3 tetrahedra surrounding every edge.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The '''pyrochoron''', also known as the '''pentachoron''' and the '''5-cell''', is the four-dimensional [[simplex]], and has the lowest possible element count of any [[flat]], non-[[degenerate]] four-dimensional shape. It consists of 5 regular tetrahedra joined at their faces, folded into 4D to form a 4D volume. It is a special case of the [[pyramid]] where the base is a [[tetrahedron]]. There are 3 tetrahedra surrounding every edge.</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 a pentachoron centered at the origin are:</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;"><blockquote>(-1, -√3/3, -√6/6, -√10/10)<br>(1, -√3/3, -√6/6, -√10/10)<br>(0, 2√3/3, -√6/6, -√10/10)<br>(0, 0, √6/2, -√10/10)<br>(0, 0, 0, 2√10/5)</blockquote></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 pentachoron 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 pentachoron with side length ''l'' are given by:</div></td></tr>
</table>Username5243http://hi.gher.space/w/index.php?title=Pyrochoron&diff=8904&oldid=prevUsername5243 at 01:37, 26 March 20172017-03-26T01:37:36Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| image=<[#embed [hash V9S3YE3HSGWFAH2J0R1YGESC6D] [width 180]]><br />[[Petrie polygon]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| image=<[#embed [hash V9S3YE3HSGWFAH2J0R1YGESC6D] [width 180]]><br />[[Petrie polygon]]</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=5, 10, 10, 5</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>| elements=5 <ins class="diffchange diffchange-inline">[[Tetrahedron|tetrahedra]]</ins>, 10 <ins class="diffchange diffchange-inline">[[triangle]]s</ins>, 10 <ins class="diffchange diffchange-inline">[[digon]]s</ins>, 5 <ins class="diffchange diffchange-inline">[[point]]s</ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc=G3PP or <nowiki>{{G3</nowiki><sup>3</sup>}<sup>4</sup>}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc=G3PP or <nowiki>{{G3</nowiki><sup>3</sup>}<sup>4</sup>}</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}{{STS Polytope</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>}}{{STS Polytope</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vfigure=[[Tetrahedron]], edge 1</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vfigure=[[Tetrahedron]], edge 1</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><blockquote>total edge length = 10''l''<br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><blockquote>total edge length = 10''l''<br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>total surface area = {{Over|5√3|2}} {{DotHV}}<br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>total surface area = {{Over|5√3|2}} {{DotHV}}<br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>surcell volume = {{Over|<del class="diffchange diffchange-inline">√2</del>|<del class="diffchange diffchange-inline">3</del>}} {{DotHV|3}}<br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>surcell volume = {{Over|<ins class="diffchange diffchange-inline">5√2</ins>|<ins class="diffchange diffchange-inline">12</ins>}} {{DotHV|3}}<br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>bulk = {{Over|√5|96}} {{DotHV|4}}</blockquote></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>bulk = {{Over|√5|96}} {{DotHV|4}}</blockquote></div></td></tr>
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</table>Username5243http://hi.gher.space/w/index.php?title=Pyrochoron&diff=8771&oldid=prevHayate: add symbol2016-03-13T11:37:11Z<p>add symbol</p>
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</table>Hayatehttp://hi.gher.space/w/index.php?title=Pyrochoron&diff=8140&oldid=prevHayate: move Bowers acronym from Template:STS Uniform polytope as it is now being used for non-uniforms too2014-03-02T09:33:36Z<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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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| dual=''Self-dual''</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| dual=''Self-dual''</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vfigure=[[Tetrahedron]], edge 1</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vfigure=[[Tetrahedron]], edge 1</div></td></tr>
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<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 '''pyrochoron''', also known as the '''pentachoron''' and the '''5-cell''', is the four-dimensional [[simplex]], and has the lowest possible element count of any [[flat]], non-[[degenerate]] four-dimensional shape. It consists of 5 regular tetrahedra joined at their faces, folded into 4D to form a 4D volume. It is a special case of the [[pyramid]] where the base is a [[tetrahedron]]. There are 3 tetrahedra surrounding every edge.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The '''pyrochoron''', also known as the '''pentachoron''' and the '''5-cell''', is the four-dimensional [[simplex]], and has the lowest possible element count of any [[flat]], non-[[degenerate]] four-dimensional shape. It consists of 5 regular tetrahedra joined at their faces, folded into 4D to form a 4D volume. It is a special case of the [[pyramid]] where the base is a [[tetrahedron]]. There are 3 tetrahedra surrounding every edge.</div></td></tr>
</table>Hayatehttp://hi.gher.space/w/index.php?title=Pyrochoron&diff=7823&oldid=prevHayate: polytope explorer integration2014-02-16T21:24:37Z<p>polytope explorer integration</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The '''pyrochoron''', also known as the '''pentachoron''' and the '''5-cell''', is the four-dimensional [[simplex]], and has the lowest possible element count of any [[flat]], non-[[degenerate]] four-dimensional shape. It consists of 5 regular tetrahedra joined at their faces, folded into 4D to form a 4D volume. It is a special case of the [[pyramid]] where the base is a [[tetrahedron]]. There are 3 tetrahedra surrounding every edge.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The '''pyrochoron''', also known as the '''pentachoron''' and the '''5-cell''', is the four-dimensional [[simplex]], and has the lowest possible element count of any [[flat]], non-[[degenerate]] four-dimensional shape. It consists of 5 regular tetrahedra joined at their faces, folded into 4D to form a 4D volume. It is a special case of the [[pyramid]] where the base is a [[tetrahedron]]. There are 3 tetrahedra surrounding every edge.</div></td></tr>
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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: #eee; color:black; font-size: smaller;"><div>=== Cell-first / vertex-first projection ===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=== Cell-first / vertex-first projection ===</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following diagram shows a perspective projection of the pentachoron.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following diagram shows a perspective projection of the pentachoron.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=== Edge-first / face-first projection ===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=== Edge-first / face-first projection ===</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The next diagram shows the pentachoron viewed at from another angle.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The next diagram shows the pentachoron viewed at from another angle.</div></td></tr>
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<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>Again, this projection represents two possible views of the pentachoron. From one view, the 4D being would see only the upper and lower tetrahedra. From the opposite view, it would see the 3 inner tetrahedra. It cannot see all 5 cells at once unless the pentachoron is transparent.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Again, this projection represents two possible views of the pentachoron. From one view, the 4D being would see only the upper and lower tetrahedra. From the opposite view, it would see the 3 inner tetrahedra. It cannot see all 5 cells at once unless the pentachoron is transparent.</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;"><[#polytope [id 36]]></ins></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Simplices|4}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Simplices|4}}</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>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Tapertope Nav|27|28|29|[11<sup>1</sup>]<sup>1</sup><br>Triangular prismic pyramid|1<sup>3</sup><br>Pentachoron|1<sup>1</sup>1<sup>1</sup><br>Duotrianglinder|chora}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Tapertope Nav|27|28|29|[11<sup>1</sup>]<sup>1</sup><br>Triangular prismic pyramid|1<sup>3</sup><br>Pentachoron|1<sup>1</sup>1<sup>1</sup><br>Duotrianglinder|chora}}</div></td></tr>
</table>Hayatehttp://hi.gher.space/w/index.php?title=Pyrochoron&diff=7588&oldid=prevHayate: K6.4 upgrade: img -> embed2014-02-11T19:40:56Z<p>K6.4 upgrade: img -> embed</p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 19:40, 11 February 2014</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><[#ontology [kind topic] [cats 4D Simplex] [alt [[freebase:02kb2x]] [[wikipedia:5-cell]]]]></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><[#ontology [kind topic] [cats 4D Simplex] [alt [[freebase:02kb2x]] [[wikipedia:5-cell]]]]></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: #ffa; color:black; font-size: smaller;"><div>| image=<[#<del class="diffchange diffchange-inline">img </del>[hash V9S3YE3HSGWFAH2J0R1YGESC6D] [width 180]]><br />[[Petrie polygon]]</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>| image=<[#<ins class="diffchange diffchange-inline">embed </ins>[hash V9S3YE3HSGWFAH2J0R1YGESC6D] [width 180]]><br />[[Petrie polygon]]</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following diagram shows a perspective projection of the pentachoron.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following diagram shows a perspective projection of the pentachoron.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The dotted line shows the far edge of the outer tetrahedron. The blue lines are inside the outer tetrahedron in this projection. The center of the projection where these blue lines meet is actually the apex of the pentachoron pointing away from us in the 4th direction.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The dotted line shows the far edge of the outer tetrahedron. The blue lines are inside the outer tetrahedron in this projection. The center of the projection where these blue lines meet is actually the apex of the pentachoron pointing away from us in the 4th direction.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following diagrams illustrate 3 of these cells.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following diagrams illustrate 3 of these cells.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Note that if a 4D being were to look at an actual pentachoron, it would not be able to see all 5 cells at once. Rather, it would either see only the outer tetrahedron (if it looks at the “base” of the pentachoron), or the 4 inner cells (if it looks at the apex of the pentachoron).</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Note that if a 4D being were to look at an actual pentachoron, it would not be able to see all 5 cells at once. Rather, it would either see only the outer tetrahedron (if it looks at the “base” of the pentachoron), or the 4 inner cells (if it looks at the apex of the pentachoron).</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The next diagram shows the pentachoron viewed at from another angle.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The next diagram shows the pentachoron viewed at from another angle.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In this diagram, three of the pentachoron's cells are arranged around the central axis indicated by the blue line. The other two cells are the upper and lower halves of the outer shape, which is called a ''trigonal bipyramid''. All the cells appear somewhat deformed from a regular tetrahedron, because they are all being viewed at from an angle. Some of these cells are shown below:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>In this diagram, three of the pentachoron's cells are arranged around the central axis indicated by the blue line. The other two cells are the upper and lower halves of the outer shape, which is called a ''trigonal bipyramid''. All the cells appear somewhat deformed from a regular tetrahedron, because they are all being viewed at from an angle. Some of these cells are shown below:</div></td></tr>
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<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>Again, this projection represents two possible views of the pentachoron. From one view, the 4D being would see only the upper and lower tetrahedra. From the opposite view, it would see the 3 inner tetrahedra. It cannot see all 5 cells at once unless the pentachoron is transparent.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Again, this projection represents two possible views of the pentachoron. From one view, the 4D being would see only the upper and lower tetrahedra. From the opposite view, it would see the 3 inner tetrahedra. It cannot see all 5 cells at once unless the pentachoron is transparent.</div></td></tr>
</table>Hayatehttp://hi.gher.space/w/index.php?title=Pyrochoron&diff=6884&oldid=prevHayate: +alt:freebase,wikipedia2012-01-10T11:52:28Z<p>+alt:freebase,wikipedia</p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 11:52, 10 January 2012</td>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><[#ontology [kind topic] [cats 4D Simplex]]></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><[#ontology [kind topic] [cats 4D Simplex<ins class="diffchange diffchange-inline">] [alt [[freebase:02kb2x]] [[wikipedia:5-cell]]</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>| image=<[#img [hash V9S3YE3HSGWFAH2J0R1YGESC6D] [width 180]]><br />[[Petrie polygon]]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| image=<[#img [hash V9S3YE3HSGWFAH2J0R1YGESC6D] [width 180]]><br />[[Petrie polygon]]</div></td></tr>
</table>Hayatehttp://hi.gher.space/w/index.php?title=Pyrochoron&diff=6590&oldid=prevHayate: fix equations2011-11-18T01:06:14Z<p>fix equations</p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 01:06, 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 pentachoron 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 pentachoron 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 = 10''l''<br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><blockquote>total edge length = 10''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"><sup></del>5√3<del class="diffchange diffchange-inline"></sup>∕<sub></del>2<del class="diffchange diffchange-inline"></sub> &middot; ''l''<sup>2</sup></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">{{Over|</ins>5√3<ins class="diffchange diffchange-inline">|</ins>2<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"><sup></del>√2<del class="diffchange diffchange-inline"></sup>∕<sub></del>3<del class="diffchange diffchange-inline"></sub> &middot; ''l''<sup></del>3<del class="diffchange diffchange-inline"></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">{{Over|</ins>√2<ins class="diffchange diffchange-inline">|</ins>3<ins class="diffchange diffchange-inline">}} {{DotHV|</ins>3<ins class="diffchange diffchange-inline">}}</ins><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"><sup></del>√5<del class="diffchange diffchange-inline"></sup>∕<sub></del>96<del class="diffchange diffchange-inline"></sub> &middot; ''l''<sup></del>4<del class="diffchange diffchange-inline"></sup></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|</ins>√5<ins class="diffchange diffchange-inline">|</ins>96<ins class="diffchange diffchange-inline">}} {{DotHV|</ins>4<ins class="diffchange diffchange-inline">}}</ins></blockquote></div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Net ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Net ==</div></td></tr>
</table>Hayatehttp://hi.gher.space/w/index.php?title=Pyrochoron&diff=6580&oldid=prevHayate: fix equations2011-11-18T00:26:12Z<p>fix equations</p>
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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 pentachoron 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 pentachoron 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 = 10''l''<br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><blockquote>total edge length = 10''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">3</del><sup><del class="diffchange diffchange-inline">2</del><sup><del class="diffchange diffchange-inline">-1</del><<del class="diffchange diffchange-inline">/sup</del>></<del class="diffchange diffchange-inline">sup</del>><del class="diffchange diffchange-inline">5</del>''l''<sup>2<del class="diffchange diffchange-inline"></sup>2<sup>-1</del></sup><br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>total surface area = <sup><ins class="diffchange diffchange-inline">5√3</ins><<ins class="diffchange diffchange-inline">/</ins>sup><ins class="diffchange diffchange-inline">∕</ins><<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">2</ins></<ins class="diffchange diffchange-inline">sub</ins>> <ins class="diffchange diffchange-inline">&middot; </ins>''l''<sup>2</sup><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">2</del><sup><del class="diffchange diffchange-inline">2</del><sup><del class="diffchange diffchange-inline">-1</del><<del class="diffchange diffchange-inline">/sup</del>></<del class="diffchange diffchange-inline">sup</del>>''l''<sup>3<del class="diffchange diffchange-inline"></sup>3<sup>-1</del></sup><br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>surcell volume = <sup><ins class="diffchange diffchange-inline">√2</ins><<ins class="diffchange diffchange-inline">/</ins>sup><ins class="diffchange diffchange-inline">∕</ins><<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">3</ins></<ins class="diffchange diffchange-inline">sub</ins>> <ins class="diffchange diffchange-inline">&middot; </ins>''l''<sup>3</sup><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">5</del><sup><del class="diffchange diffchange-inline">2</del><sup><del class="diffchange diffchange-inline">-1</del><<del class="diffchange diffchange-inline">/sup</del>></<del class="diffchange diffchange-inline">sup</del>>''l''<sup>4<del class="diffchange diffchange-inline"></sup>96<sup>-1</del></sup></blockquote></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>bulk = <sup><ins class="diffchange diffchange-inline">√5</ins><<ins class="diffchange diffchange-inline">/</ins>sup><ins class="diffchange diffchange-inline">∕</ins><<ins class="diffchange diffchange-inline">sub</ins>><ins class="diffchange diffchange-inline">96</ins></<ins class="diffchange diffchange-inline">sub</ins>> <ins class="diffchange diffchange-inline">&middot; </ins>''l''<sup>4</sup></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>== Net ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Net ==</div></td></tr>
</table>Hayatehttp://hi.gher.space/w/index.php?title=Pyrochoron&diff=6512&oldid=prevHayate at 20:35, 12 March 20112011-03-12T20:35:21Z<p></p>
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<td colspan='2' style="background-color: white; color:black;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black;">Revision as of 20:35, 12 March 2011</td>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| dual=''Self-dual''</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| dual=''Self-dual''</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: #ffa; color:black; font-size: smaller;"><div>| vfigure=[[<del class="diffchange diffchange-inline">テ</del>]], edge 1</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>]], edge 1</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vlayout=([[Triangle|3]][[Tetrahedron|<sup>3</sup>]])<sup>4</sup></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| vlayout=([[Triangle|3]][[Tetrahedron|<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>| bowers=Pen</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| bowers=Pen</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=ペン</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>
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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: #eee; color:black; font-size: smaller;"><div>{{Tapertope Nav|27|28|29|[11<sup>1</sup>]<sup>1</sup><br>Triangular prismic pyramid|1<sup>3</sup><br>Pentachoron|1<sup>1</sup>1<sup>1</sup><br>Duotrianglinder|chora}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Tapertope Nav|27|28|29|[11<sup>1</sup>]<sup>1</sup><br>Triangular prismic pyramid|1<sup>3</sup><br>Pentachoron|1<sup>1</sup>1<sup>1</sup><br>Duotrianglinder|chora}}</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;">[[Category:Regular polychora]]</del></div></td><td colspan="2"> </td></tr>
</table>Hayate