forum.polymake.org

Posted: **16 Feb 2015, 20:33**

Let F be a face of a polytope P. Is it possible to construct the face figure P/F in polymake?

I'd like to construct all the face figures of P. My code is

Code: Select all

sub faceFigures {
    my ($p)  = @_;
    my $v    = $p -> VERTICES;
    my $hd   = $p -> HASSE_DIAGRAM;
    my $dim  = $p -> DIM;                                                                          

    for (my $d = $dim; $d >= 0; --$d) {
        foreach (@{$hd -> nodes_of_dim($d)}) {
            my $f  = new Polytope<Rational>(VERTICES=>$v->minor($hd->FACES->[$_],All));
            my $fd = polarize( center($f) );     
            print $fd -> DIM;                                
        }                                                                      
    }                                                                                     
}

I'm getting incorrect results (I'm getting incorrect dimensions of P/F).

Posted: **16 Feb 2015, 23:00**

First, there is nothing to compute the face figure directly.

Second, the polar of a polytope with non-zero codimension might have a lineality space corresponding (i.e. orthogonal) to the affine hull of the original polytope.
("might" because there seems to be a discrepancy / bug between the documentation and some of the code in polarize which we will look into)

You can make sure to get the right thing by taking the pointed_part:

Code: Select all

my $fd = pointed_part( polarize( center($f) ) );

Benjamin

Posted: **16 Feb 2015, 23:07**

Thanks (again!) Benjamin.

Would projecting center($f) onto a full-dimensional polytope also do the trick?

Posted: **16 Feb 2015, 23:11**

Yes that should do the trick as well, there is a projection_full client for it. But the resulting polytopes wont live in the same ambient space anymore.

Posted: **16 Feb 2015, 23:14**

Ok.

Basically I'm trying to compute the g-polynomial of the poset [F,P] and the only way I can think of doing it is by computing the G_VECTOR of P/F. Modifying the ambient dimension doesn't change the polytope from a combinatorial perspective so this should work.

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Is it possible to construct the face figure P/F in polymake?

Is it possible to construct the face figure P/F in polymake?

Re: Is it possible to construct the face figure P/F in polymake?

Re: Is it possible to construct the face figure P/F in polymake?

Re: Is it possible to construct the face figure P/F in polymake?

Re: Is it possible to construct the face figure P/F in polymake?