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Warning: Cannot modify header information - headers already sent by (output started at /var/www/vhosts/oskarvandeventer.nl/twistypedia.oskarvandeventer.nl/includes/session/Session.php:48) in /var/www/vhosts/oskarvandeventer.nl/twistypedia.oskarvandeventer.nl/includes/WebResponse.php on line 74 http://twistypedia.oskarvandeventer.nl/index.php?action=history&feed=atom&title=Imaginary_PieceImaginary Piece - Revision history2026-05-13T22:59:48ZRevision history for this page on the wikiMediaWiki 1.36.1http://twistypedia.oskarvandeventer.nl/index.php?title=Imaginary_Piece&diff=214&oldid=prevWwwmwww at 05:16, 18 August 20132013-08-18T05:16:03Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 05:16, 18 August 2013</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The set of pieces defined by Matt Galla's analysis of twistability that exist outside the set of [[Real Piece|real physical pieces]]. This is discussed in this thread but Matt uses a totally different analysis. He makes no assumption of a holding point and instead looks at all possible way a piece CAN move. For example he looks at pieces that move with BOTH the L and R layers on a 3x3x3. Such pieces doesn't exist in Andreas's method. But Matt goes on to prove such pieces "MUST exist mathematically". While not immediately obvious it turns out the Imaginary Pieces are a superset of the Virtial Pieces. Andreas now prefers the term NHP for Non-Holding Point over Imaginary.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The set of pieces defined by Matt Galla's analysis of twistability that exist outside the set of [[Real Piece|real physical pieces]]. This is discussed in <ins style="font-weight: bold; text-decoration: none;">[http://twistypuzzles.com/forum/viewtopic.php?f=1&t=15667 </ins>this thread<ins style="font-weight: bold; text-decoration: none;">] </ins>but Matt <ins style="font-weight: bold; text-decoration: none;">who </ins>uses a totally different analysis <ins style="font-weight: bold; text-decoration: none;">then Andreas</ins>. He makes no assumption of a <ins style="font-weight: bold; text-decoration: none;">[[Holding Point|</ins>holding point<ins style="font-weight: bold; text-decoration: none;">]] </ins>and instead looks at all possible way a piece CAN move. For example he looks at pieces that move with BOTH the L and R layers on a 3x3x3. Such pieces doesn't exist in Andreas's method. But Matt goes on to prove such pieces "MUST exist mathematically". While not immediately obvious it turns out the Imaginary Pieces are a superset of the <ins style="font-weight: bold; text-decoration: none;">[[Virtual Piece|</ins>Virtial Pieces<ins style="font-weight: bold; text-decoration: none;">]]</ins>. Andreas now prefers the term <ins style="font-weight: bold; text-decoration: none;">[[NHP|</ins>NHP<ins style="font-weight: bold; text-decoration: none;">]] </ins>for Non-Holding Point over Imaginary.</div></td></tr>
</table>Wwwmwwwhttp://twistypedia.oskarvandeventer.nl/index.php?title=Imaginary_Piece&diff=213&oldid=prevWwwmwww: Created page with "The set of pieces defined by Matt Galla's analysis of twistability that exist outside the set of real physical pieces. This is discussed in this thread but Matt..."2013-08-18T05:12:29Z<p>Created page with "The set of pieces defined by Matt Galla's analysis of twistability that exist outside the set of <a href="/index.php?title=Real_Piece" title="Real Piece">real physical pieces</a>. This is discussed in this thread but Matt..."</p>
<p><b>New page</b></p><div>The set of pieces defined by Matt Galla's analysis of twistability that exist outside the set of [[Real Piece|real physical pieces]]. This is discussed in this thread but Matt uses a totally different analysis. He makes no assumption of a holding point and instead looks at all possible way a piece CAN move. For example he looks at pieces that move with BOTH the L and R layers on a 3x3x3. Such pieces doesn't exist in Andreas's method. But Matt goes on to prove such pieces "MUST exist mathematically". While not immediately obvious it turns out the Imaginary Pieces are a superset of the Virtial Pieces. Andreas now prefers the term NHP for Non-Holding Point over Imaginary.</div>Wwwmwww