user_guide:tutorials:latest:pcom

# Differences

This shows you the differences between two versions of the page.

 — user_guide:tutorials:latest:pcom [2020/01/22 09:02] (current) Line 1: Line 1: + ==== Polyhedral complexes in polymake ==== + + Polyhedral complexes are contained in the application ''​fan'',​ so you hanve to switch application to access the full functionality. + + + > application "​fan";​ + ​ + 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. + + + > $pc1 = new PolyhedralComplex(POINTS=>​[[1,​0,​0],​[1,​0,​1],​[1,​1,​0],​[1,​1,​1]],​INPUT_POLYTOPES=>​[[0,​1,​2],​[2,​3],​[1]]);​ + ​ + Since some of the input polytopes may be redundant, you should ask for the ''​MAXIMAL_POLYTOPES''​. + + + > print$pc1->​MAXIMAL_POLYTOPES;​ + {0 1 2} + {2 3} + ​ + {{ :​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: + + + > $c=cube(3); + >$triangulation=new PolyhedralComplex(VERTICES=>​$c->​VERTICES,​MAXIMAL_POLYTOPES=>​$c->​TRIANGULATION->​FACETS);​ + ​ + === 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