VERTICES_IN_FACETS and orientation

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i96
Posts: 10
Joined: 03 Apr 2015, 12:41

VERTICES_IN_FACETS and orientation

Postby i96 » 28 Apr 2015, 20:04

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.

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joswig
Main Author
Posts: 280
Joined: 24 Dec 2010, 11:10

Re: VERTICES_IN_FACETS and orientation

Postby joswig » 28 Apr 2015, 22:01

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

i96
Posts: 10
Joined: 03 Apr 2015, 12:41

Re: VERTICES_IN_FACETS and orientation

Postby i96 » 28 Apr 2015, 23:35

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!


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