pcom:pc1

==== 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}
> $pc1->VISUAL;

pcom:pc1

Explode

Automatic explosion

Exploding speed

Transparency

Rotation

x-axis

y-axis

z-axis

Rotation speed

Display

Objects

Camera

SVG

=== 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.