user_guide:tutorials:pcom

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user_guide:tutorials:pcom [2019/01/25 09:27]
oroehrig ↷ Links adapted because of a move operation
user_guide:tutorials:pcom [2019/02/04 22:55] (current)
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-==== Polyhedral complexes in polymake ====+{{page>​.:​latest:​@FILEID@}}
  
-Polyhedral complexes are contained in the application ''​fan'',​ so you hanve to switch application to access the full functionality. 
-<​code>​ 
-> 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>​ 
-fan > $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>​ 
-fan > print $pc1->​MAXIMAL_POLYTOPES;​ 
-{0 1 2} 
-{2 3} 
-</​code>​ 
- 
-{{ user_guide:​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>​ 
-fan > $c=cube(3); 
-fan > $triangulation=new PolyhedralComplex(VERTICES=>​$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/pcom.txt
  • Last modified: 2019/02/04 22:55
  • (external edit)