VERTICES_IN_FACETS and orientation
Posted: 28 Apr 2015, 20:04
by i96
If $c is a polytope, then $c->VERTICES_IN_FACETS contains the lists of vertices. Any list is sorted in ascending order. Since the polytope is oriented, for all the lists we also have another order (up to rotations), induced by this orientation.
Is there a way to find it via polymake?
Thanks a lot.
Re: VERTICES_IN_FACETS and orientation
Posted: 28 Apr 2015, 22:01
by joswig
I presume you are talking about 3-dimensional polytopes? For those you can get a consistent orientation of the facets as follows:
Code: Select all
polytope > print pyramid(cube(2))->VIF_CYCLIC_NORMAL;
0 4 2
3 4 1
0 1 4
2 4 3
0 2 3 1
Re: VERTICES_IN_FACETS and orientation
Posted: 28 Apr 2015, 23:35
by i96
I presume you are talking about 3-dimensional polytopes? For those you can get a consistent orientation of the facets as follows:
Code: Select all
polytope > print pyramid(cube(2))->VIF_CYCLIC_NORMAL;
0 4 2
3 4 1
0 1 4
2 4 3
0 2 3 1
Yes, I have meant polyhedra. Thank you!