forum.polymake.org

Hi,

Is there a way to get a maximum affinely independet subset of the vertices, which are incident to a facet? (I only know of VERTICES_IN_FACETS, where one gets all vertices)

Best regards,
Markus

There is no direct way, but the function basis_rows(Matrix) returns a basis of a matrix. As the vertices are homogeneous this will return an affinely independent set if you apply this to the vertices of a facet of a polytope.

Note however, that the function returns a list of indices referring to the rows of the input matrix, so if you do something like the returned lists gives indices relative to the list in $p->VERTICES_IN_FACETS->[0]. One option to convert this into a list referring to VERTICES is to turn $p->VERTICES_IN_FACETS->[0] into a perl array and map out the elements indexed by the basis.