user_guide:tutorials:face_lattice_tutorial

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tutorial:face_lattice_tutorial [2012/05/22 11:57] – [Dealing with Large Polytopes] joswigtutorial:face_lattice_tutorial [2014/01/03 15:45] – external edit 127.0.0.1
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-The executive summary: While polymake is designed to to all kinds of things automatically, you might have to guide it a little if you are computing with large or special input.+The executive summary: While polymake is designed to do all kinds of things automatically, you might have to guide it a little if you are computing with large or special input.
  
 One more caveat:  A //d//-polytope with //n// vertices has at most //O(n^(d/2))// facets.  This is the consequence of the Upper-Bound-Theorem. One more caveat:  A //d//-polytope with //n// vertices has at most //O(n^(d/2))// facets.  This is the consequence of the Upper-Bound-Theorem.
   * McMullen, Peter:  The maximum numbers of faces of a convex polytope. Mathematika 17 (1970) 179-184.   * McMullen, Peter:  The maximum numbers of faces of a convex polytope. Mathematika 17 (1970) 179-184.
 This number is actually attained by neighborly polytopes; for example, by the cyclic polytopes. This number is actually attained by neighborly polytopes; for example, by the cyclic polytopes.
  • user_guide/tutorials/face_lattice_tutorial.txt
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