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--- user_guide:tutorials:pcom [2019/01/25 09:38] – ↷ Page moved from user_guide:pcom to user_guide:tutorials:pcom oroehrig
+++ user_guide:tutorials:pcom [2019/02/04 22:55] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
-==== 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.