http://hi.gher.space/w/index.php?title=Cubinder&feed=atom&action=historyCubinder - Revision history2024-03-29T06:32:52ZRevision history for this page on the wikiMediaWiki 1.16.2http://hi.gher.space/w/index.php?title=Cubinder&diff=9010&oldid=prevIcebreaker at 09:12, 19 June 20182018-06-19T09:12:39Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The net of a cubinder is a square prism surrounded by four cylinders:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The net of a cubinder is a square prism surrounded by four cylinders:</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><blockquote><[#embed [hash <del class="diffchange diffchange-inline">RPQ54H9ZJ1S4WA06VMPAT4YKTJ</del>]]></blockquote></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><blockquote><[#embed [hash <ins class="diffchange diffchange-inline">6XMAYS6F8E9MYP67GCF9YR0D79</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>== Cross-sections ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>== Cross-sections ==</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Round cell-first:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Round cell-first:</div></td></tr>
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<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>Cylinder-first:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Cylinder-first:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Disk-first:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Disk-first:</div></td></tr>
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<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>Round face-first:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Round face-first:</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:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Edge-first:</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>
</table>Icebreakerhttp://hi.gher.space/w/index.php?title=Cubinder&diff=9003&oldid=prevIcebreaker at 16:58, 24 April 20182018-04-24T16:58:21Z<p></p>
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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>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>The net of a cubinder is a <del class="diffchange diffchange-inline">[[cube]] </del>surrounded by four cylinders:</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>The net of a cubinder is a <ins class="diffchange diffchange-inline">square prism </ins>surrounded by four cylinders:</div></td></tr>
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<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">== Cross-sections ==</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 colspan="2"> </td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">Round cell-first:</ins></div></td></tr>
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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 class="diffchange diffchange-inline">Round face-first:</ins></div></td></tr>
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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 class="diffchange diffchange-inline">Edge-first:</ins></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>
</table>Icebreakerhttp://hi.gher.space/w/index.php?title=Cubinder&diff=8945&oldid=prevUsername5243: /* Equations */2017-03-26T14:50:14Z<p><span class="autocomment">Equations</span></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*Variables:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*Variables:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><blockquote>''r'' ⇒ radius of the cubinder<br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><blockquote>''r'' ⇒ radius of the cubinder<br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>''<del class="diffchange diffchange-inline">a</del>'' ⇒ height of the cubinder along z<del class="diffchange diffchange-inline">-axis <br></del></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>''<ins class="diffchange diffchange-inline">h</ins>'' ⇒ height of the cubinder along z <ins class="diffchange diffchange-inline">and </ins>w <ins class="diffchange diffchange-inline">axes</ins></blockquote></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del class="diffchange diffchange-inline">''b'' ⇒ tridth of the cubinder along </del>w<del class="diffchange diffchange-inline">-axis</del></blockquote></div></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;"></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>*All points (''x'', ''y'', ''z'', ''w'') that lie on the [[surcell]] of a cubinder will satisfy the following equations:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*All points (''x'', ''y'', ''z'', ''w'') that lie on the [[surcell]] of a cubinder will satisfy the following equations:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><blockquote>''x''<sup>2</sup> + ''y''<sup>2</sup> = ''r''<sup>2</sup> <br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><blockquote>''x''<sup>2</sup> + ''y''<sup>2</sup> = ''r''<sup>2</sup> <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>abs(''z'') ≤ ''<del class="diffchange diffchange-inline">a</del>'' <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>abs(''z'') ≤ ''<ins class="diffchange diffchange-inline">h</ins>'' <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>abs(''w'') ≤ ''<del class="diffchange diffchange-inline">b</del>'' <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>abs(''w'') ≤ ''<ins class="diffchange diffchange-inline">h</ins>'' <br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&nbsp;&nbsp;&nbsp;-- or --<br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>&nbsp;&nbsp;&nbsp;-- or --<br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''x''<sup>2</sup> + ''y''<sup>2</sup> < ''r''<sup>2</sup> <br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>''x''<sup>2</sup> + ''y''<sup>2</sup> < ''r''<sup>2</sup> <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>abs(''z'') = ''<del class="diffchange diffchange-inline">a</del>'' <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>abs(''z'') = ''<ins class="diffchange diffchange-inline">h</ins>'' <br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>abs(''w'') = ''<del class="diffchange diffchange-inline">b</del>'' <br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>abs(''w'') = ''<ins class="diffchange diffchange-inline">h</ins>'' <br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></blockquote></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></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>*The [[hypervolume]]s of a cubinder 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 cubinder 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 = 8π''r''<br></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div><blockquote>total edge length = 8π''r''<br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>total surface area = 4π''r''(''r'' + ''<del class="diffchange diffchange-inline">a'' + ''b</del>'')<br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>total surface area = 4π''r''(''r'' + <ins class="diffchange diffchange-inline">2</ins>''<ins class="diffchange diffchange-inline">h</ins>'')<br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>surcell volume = 2π''r''(''<del class="diffchange diffchange-inline">ra</del>'' + ''<del class="diffchange diffchange-inline">rb'' + ''ab</del>'')<br></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>surcell volume = 2π''r''(''<ins class="diffchange diffchange-inline">rh</ins>'' + ''<ins class="diffchange diffchange-inline">h</ins>''<ins class="diffchange diffchange-inline"><sup>2</sup></ins>)<br></div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>bulk = π''r''<sup>2</sup>''<del class="diffchange diffchange-inline">ab</del>''</blockquote></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>bulk = π''r''<sup>2</sup>''<ins class="diffchange diffchange-inline">h</ins>''<ins class="diffchange diffchange-inline"><sup>2</sup></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>*The [[realmic]] [[cross-section]]s (''n'') of a cubinder are:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*The [[realmic]] [[cross-section]]s (''n'') of a cubinder are:</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><blockquote>[!x,!y] ⇒ square cuboid</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><blockquote>[!x,!y] ⇒ square cuboid<ins class="diffchange diffchange-inline"><br></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[!z,!w] ⇒ cylinder</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>[!z,!w] ⇒ cylinder</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></blockquote></div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div></blockquote></div></td></tr>
</table>Username5243http://hi.gher.space/w/index.php?title=Cubinder&diff=8914&oldid=prevUsername5243 at 02:27, 26 March 20172017-03-26T02:27:57Z<p></p>
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<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=<del class="diffchange diffchange-inline">5</del>, <del class="diffchange diffchange-inline">8</del>, 4, 0</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>| elements=<ins class="diffchange diffchange-inline">4 [[cylinder]]s</ins>, <ins class="diffchange diffchange-inline">1 square hose, 4 [[circle]]s, 4 hoses</ins>, 4 <ins class="diffchange diffchange-inline">circular edges</ins>, 0</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc2=++T2</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc2=++T2</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>| pv_square=<del class="diffchange diffchange-inline">~</del><sup>π</sup>⁄<sub>4</sub> ≈ 0.7854</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>| pv_square=<sup>π</sup>⁄<sub>4</sub> ≈ 0.7854</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>A '''cubinder''' is a special case of a [[prism]] where the base is a [[cylinder]]. It is also the limiting shape of an n,4-[[duoprism]] as n approaches infinity. In other words, it is the [[Cartesian product]] of a [[circle]] and a [[square]].</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>A '''cubinder''' is a special case of a [[prism]] where the base is a [[cylinder]]. It is also the limiting shape of an n,4-[[duoprism]] as n approaches infinity. In other words, it is the [[Cartesian product]] of a [[circle]] and a [[square]].</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*The [[realmic]] [[cross-section]]s (''n'') of a cubinder are:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>*The [[realmic]] [[cross-section]]s (''n'') of a cubinder are:</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><blockquote><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><blockquote><ins class="diffchange diffchange-inline">[!x,!y] ⇒ square cuboid</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">[!z,!w] ⇒ cylinder</ins></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>Username5243http://hi.gher.space/w/index.php?title=Cubinder&diff=7620&oldid=prevHayate: K6.4 upgrade: img -> embed2014-02-11T19:46:21Z<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>The net of a cubinder is a [[cube]] surrounded by four cylinders:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The net of a cubinder is a [[cube]] surrounded by four cylinders:</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>The cubical cylinder, or cubinder for short, is one of the ways to generalize the 3D cylinder to 4D. This object can be constructed by extruding a 3D cylinder along the W-axis by a unit distance. The following is a diagram of the cubinder in parallel projection:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The cubical cylinder, or cubinder for short, is one of the ways to generalize the 3D cylinder to 4D. This object can be constructed by extruding a 3D cylinder along the W-axis by a unit distance. The following is a diagram of the cubinder in parallel 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 is a perspective projection of the cubinder:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following is a perspective projection of the cubinder:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The inner cylinder is actually the same size as the outer cylinder, but appears smaller in perspective because it is farther away. Also, the upper and lower frustums connecting the inner cylinder to the outer cylinder are actually themselves regular cylinders; but they appear as frustums because they are being viewed at from an angle.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The inner cylinder is actually the same size as the outer cylinder, but appears smaller in perspective because it is farther away. Also, the upper and lower frustums connecting the inner cylinder to the outer cylinder are actually themselves regular cylinders; but they appear as frustums because they are being viewed at from an angle.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>And the next diagram shows another perspective projection, this time with the cubinder rotated 45 degrees in the ZW plane.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>And the next diagram shows another perspective projection, this time with the cubinder rotated 45 degrees in the ZW plane.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Here, it is more apparent that the cubinder consists of four 3D cylinders joined at their circular ends. What is not so apparent, however, is that their round surfaces are joined by a square torus. This is the torus generated by rotating a square in the ZW plane (displaced in the Y direction by one unit) in the XY plane. One could also construct it by extruding the round part of the cylinder along the W-axis.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Here, it is more apparent that the cubinder consists of four 3D cylinders joined at their circular ends. What is not so apparent, however, is that their round surfaces are joined by a square torus. This is the torus generated by rotating a square in the ZW plane (displaced in the Y direction by one unit) in the XY plane. One could also construct it by extruding the round part of the cylinder along the W-axis.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The reason for the cubinder's name is that one of its possible projections is the 3D cube:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The reason for the cubinder's name is that one of its possible projections is the 3D cube:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The blue edges in the cube show where the 4 circular ends of the cylinders are. They have collapsed into a single line in the diagram because they are perpendicular to the direction of projection.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The blue edges in the cube show where the 4 circular ends of the cylinders are. They have collapsed into a single line in the diagram because they are perpendicular to the direction of projection.</div></td></tr>
</table>Hayatehttp://hi.gher.space/w/index.php?title=Cubinder&diff=7338&oldid=prevHayate: toracubinder -> spheritorus2014-02-02T18:57:25Z<p>toracubinder -> spheritorus</p>
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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|14|15|16|22<br>Duocylinder|211<br>Cubinder|1111<br>Tesseract|chora}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Tapertope Nav|14|15|16|22<br>Duocylinder|211<br>Cubinder|1111<br>Tesseract|chora}}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{Toratope Nav A|4|5|6|IIII<br>Tesseract|(IIII)<br>Glome|(II)II<br>Cubinder|((II)II)<br><del class="diffchange diffchange-inline">Toracubinder</del>|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|chora}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>{{Toratope Nav A|4|5|6|IIII<br>Tesseract|(IIII)<br>Glome|(II)II<br>Cubinder|((II)II)<br><ins class="diffchange diffchange-inline">Spheritorus</ins>|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|chora}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Bracketope Nav|12|13|14|(IIII)<br>Glome|[(II)II]<br>Cubinder|<(II)II><br>Dibicone|chora}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Bracketope Nav|12|13|14|(IIII)<br>Glome|[(II)II]<br>Cubinder|<(II)II><br>Dibicone|chora}}</div></td></tr>
</table>Hayatehttp://hi.gher.space/w/index.php?title=Cubinder&diff=6652&oldid=prevHayate: update bracketope nav2011-11-18T16:26:48Z<p>update bracketope nav</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Toratope Nav A|4|5|6|IIII<br>Tesseract|(IIII)<br>Glome|(II)II<br>Cubinder|((II)II)<br>Toracubinder|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|chora}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Toratope Nav A|4|5|6|IIII<br>Tesseract|(IIII)<br>Glome|(II)II<br>Cubinder|((II)II)<br>Toracubinder|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|chora}}</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>{{Bracketope Nav|<del class="diffchange diffchange-inline">15</del>|<del class="diffchange diffchange-inline">16</del>|<del class="diffchange diffchange-inline">17</del>|<del class="diffchange diffchange-inline">[<xy>zw]</del><br><del class="diffchange diffchange-inline">Narrow tesseract</del>|[(<del class="diffchange diffchange-inline">xy</del>)<del class="diffchange diffchange-inline">zw</del>]<br>Cubinder|<del class="diffchange diffchange-inline">[</del><<del class="diffchange diffchange-inline">[xy]z</del>><del class="diffchange diffchange-inline">w]</del><br><del class="diffchange diffchange-inline">Wide octahedral prism</del>|chora}}</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>{{Bracketope Nav|<ins class="diffchange diffchange-inline">12</ins>|<ins class="diffchange diffchange-inline">13</ins>|<ins class="diffchange diffchange-inline">14</ins>|<ins class="diffchange diffchange-inline">(IIII)</ins><br><ins class="diffchange diffchange-inline">Glome</ins>|[(<ins class="diffchange diffchange-inline">II</ins>)<ins class="diffchange diffchange-inline">II</ins>]<br>Cubinder|<<ins class="diffchange diffchange-inline">(II)II</ins>><br><ins class="diffchange diffchange-inline">Dibicone</ins>|chora}}</div></td></tr>
</table>Hayatehttp://hi.gher.space/w/index.php?title=Cubinder&diff=6552&oldid=prevHayate at 22:35, 12 March 20112011-03-12T22:35:45Z<p></p>
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<td colspan='2' style="background-color: white; color:black;">Revision as of 22:35, 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 Curved Rotatope]]></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>| name=Cubinder</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| name=Cubinder</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Toratope Nav A|4|5|6|IIII<br>Tesseract|(IIII)<br>Glome|(II)II<br>Cubinder|((II)II)<br>Toracubinder|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|chora}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Toratope Nav A|4|5|6|IIII<br>Tesseract|(IIII)<br>Glome|(II)II<br>Cubinder|((II)II)<br>Toracubinder|(II)(II)<br>Duocylinder|((II)(II))<br>Tiger|chora}}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Bracketope Nav|15|16|17|[<xy>zw]<br>Narrow tesseract|[(xy)zw]<br>Cubinder|[<[xy]z>w]<br>Wide octahedral prism|chora}}</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>{{Bracketope Nav|15|16|17|[<xy>zw]<br>Narrow tesseract|[(xy)zw]<br>Cubinder|[<[xy]z>w]<br>Wide octahedral prism|chora}}</div></td></tr>
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</table>Hayatehttp://hi.gher.space/w/index.php?title=Cubinder&diff=6298&oldid=prevHayate: fix images2011-03-08T21:38:57Z<p>fix images</p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The net of a cubinder is a [[cube]] surrounded by four cylinders:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The net of a cubinder is a [[cube]] surrounded by four cylinders:</div></td></tr>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><blockquote><del class="diffchange diffchange-inline">http://teamikaria.com/dl/L-ITkCK7eFiOCajCs2hl4xZRQ0XAB31ua64QFKaw0OB4rMPa.png</del></blockquote></div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><blockquote><ins class="diffchange diffchange-inline"><[#img [hash E1DEP0C53JK6MRZHKYP1RVJ3AW]]></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>== 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>The cubical cylinder, or cubinder for short, is one of the ways to generalize the 3D cylinder to 4D. This object can be constructed by extruding a 3D cylinder along the W-axis by a unit distance. The following is a diagram of the cubinder in parallel projection:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The cubical cylinder, or cubinder for short, is one of the ways to generalize the 3D cylinder to 4D. This object can be constructed by extruding a 3D cylinder along the W-axis by a unit distance. The following is a diagram of the cubinder in parallel 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 is a perspective projection of the cubinder:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The following is a perspective projection of the cubinder:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The inner cylinder is actually the same size as the outer cylinder, but appears smaller in perspective because it is farther away. Also, the upper and lower frustums connecting the inner cylinder to the outer cylinder are actually themselves regular cylinders; but they appear as frustums because they are being viewed at from an angle.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The inner cylinder is actually the same size as the outer cylinder, but appears smaller in perspective because it is farther away. Also, the upper and lower frustums connecting the inner cylinder to the outer cylinder are actually themselves regular cylinders; but they appear as frustums because they are being viewed at from an angle.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>And the next diagram shows another perspective projection, this time with the cubinder rotated 45 degrees in the ZW plane.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>And the next diagram shows another perspective projection, this time with the cubinder rotated 45 degrees in the ZW plane.</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>Here, it is more apparent that the cubinder consists of four 3D cylinders joined at their circular ends. What is not so apparent, however, is that their round surfaces are joined by a square torus. This is the torus generated by rotating a square in the ZW plane (displaced in the Y direction by one unit) in the XY plane. One could also construct it by extruding the round part of the cylinder along the W-axis.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>Here, it is more apparent that the cubinder consists of four 3D cylinders joined at their circular ends. What is not so apparent, however, is that their round surfaces are joined by a square torus. This is the torus generated by rotating a square in the ZW plane (displaced in the Y direction by one unit) in the XY plane. One could also construct it by extruding the round part of the cylinder along the W-axis.</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The reason for the cubinder's name is that one of its possible projections is the 3D cube:</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The reason for the cubinder's name is that one of its possible projections is the 3D cube:</div></td></tr>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The blue edges in the cube show where the 4 circular ends of the cylinders are. They have collapsed into a single line in the diagram because they are perpendicular to the direction of projection.</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>The blue edges in the cube show where the 4 circular ends of the cylinders are. They have collapsed into a single line in the diagram because they are perpendicular to the direction of projection.</div></td></tr>
</table>Hayatehttp://hi.gher.space/w/index.php?title=Cubinder&diff=6160&oldid=prevHayate at 00:22, 8 December 20102010-12-08T00:22:22Z<p></p>
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<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc=[(xy)zw]</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc=[(xy)zw]</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc2=++T2</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| ssc2=++T2</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>| pv_square=~<del class="diffchange diffchange-inline">π⁄4 </del>≈ 0.7854</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>| pv_square=~<ins class="diffchange diffchange-inline"><sup>π</sup>⁄<sub>4</sub> </ins>≈ 0.7854</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| extra={{STS Tapertope</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| extra={{STS Tapertope</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| order=3, 0</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>| order=3, 0</div></td></tr>
</table>Hayate