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--- tutorial:pcom [2011/05/05 10:30] – kulas
+++ user_guide:tutorials:pcom [2019/01/25 09:38] – ↷ Page moved from user_guide:pcom to user_guide:tutorials:pcom oroehrig
@@ Line 1: / Line 1: @@
-Polyhedral complexes are contained in the application ''fan''. There are two ways to define polyhedral complexes in ''polymake''. First, a polyhedral complex can be defined by an array of input points and, firstly, by a list of polytopes or, secondly, by a list of cells. In both cases the indices refer to the given points. The distinction between them is done due to the definition of [[regular_subdivisions|regular subdivisions]], where a point projected back to the subdivision may be an inner point of a cell and not a vertex of it. In both cases the indices refer to the given points.
+==== Polyhedral complexes in polymake ====
+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]]);
-fan > $pc2 = new PolyhedralComplex(POINTS=>[[1,0],[1,1],[1,2]], MAXIMAL_CELLS=>[[0,2],[0,1,2]]);
 </code>
@@ Line 9: / Line 14: @@
 <code>
-fan > print $pc->MAXIMAL_POLYTOPES;
+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.