user_guide:tutorials:latest:pcom

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user_guide:tutorials:latest:pcom [2020/01/22 09:02] (current)
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 +==== Polyhedral complexes in polymake ====
 +
 +Polyhedral complexes are contained in the application ''​fan'',​ so you hanve to switch application to access the full functionality.
 +
 +<code perl>
 +> application "​fan";​
 +</​code>​
 +To define polyhedral complexes in ''​polymake'',​ you need to provide an array of input points and a list of polytopes represented as an array of arrays of point indices.
 +
 +<code perl>
 +> $pc1 = new PolyhedralComplex(POINTS=>​[[1,​0,​0],​[1,​0,​1],​[1,​1,​0],​[1,​1,​1]],​INPUT_POLYTOPES=>​[[0,​1,​2],​[2,​3],​[1]]);​
 +</​code>​
 +Since some of the input polytopes may be redundant, you should ask for the ''​MAXIMAL_POLYTOPES''​.
 +
 +<code perl>
 +> print $pc1->​MAXIMAL_POLYTOPES;​
 +{0 1 2}
 +{2 3}
 +</​code>​
 +{{ :​tutorial:​pcom2.png }}
 +
 +=== Triangulations ===
 +
 +Triangulations of polytopes form an important special class of polytopal complexes. In polymake they are objects of type ''​SimplicialComplex''​ (and thus belong to the application ''​topaz''​). However, it is easy to convert them as follows:
 +
 +<code perl>
 +> $c=cube(3);
 +> $triangulation=new PolyhedralComplex(VERTICES=>​$c->​VERTICES,​MAXIMAL_POLYTOPES=>​$c->​TRIANGULATION->​FACETS);​
 +</​code>​
 +=== Voronoi Diagrams and regular subdivisions ===
 +
 +There are seperate tutorials for [[voronoi|Voronoi diagrams]] and [[regular_subdivisions|regluar subdivisions]] of point sets.
 +
  
  • user_guide/tutorials/latest/pcom.txt
  • Last modified: 2020/01/22 09:02
  • (external edit)