Regular subdivisons of point configurations
Posted: 12 Nov 2012, 11:58
by aurelien
I would like to compute the regular subdivision of a polytope. I've been trying to follow the tutorial here
http://www.polymake.org/doku.php/tutori ... bdivisions
but the instructions seem to be for an older version of polymake. I am using version 2.12.
How is the regular subdivision of a polytope computed in version 2.12?
Thank you
Re: Regular subdivisons of point configurations
Posted: 12 Nov 2012, 18:19
by joswig
Please use the function regular_subdivision:
Code: Select all
polytope > help "regular_subdivision";
functions/Subdivisions/regular_subdivision:
regular_subdivision(points, weights) -> Array<Set<Int>>
Compute a regular subdivision of the polytope obtained
by lifting points to weights and taking the lower
complex of the resulting polytope.
If the weight is generic the output is a triangulation.
Arguments:
Matrix points
Vector weights
Returns Array<Set<Int>>
To produce a suitable "big" object, you can do, for instance:
Code: Select all
polytope > $Pts=cube(2)->VERTICES;
polytope > $C=new fan::PolyhedralComplex(POINTS=>$Pts,MAXIMAL_CELLS=>regular_subdivision($Pts,new Vector([0,0,0,1])));
Then you can try like
Code: Select all
polytope > print $C->MAXIMAL_CELLS;
{1 2 3}
{0 1 2}
polytope > $C->VISUAL;
Re: Regular subdivisons of point configurations
Posted: 13 Nov 2012, 13:51
by aurelien
Great, thanks for the quick response.