ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 27 Aug 2019 11:22:20 -0500Forming a polytope from only its combinatorial datahttp://ask.sagemath.org/question/34327/forming-a-polytope-from-only-its-combinatorial-data/ I would like to visualize a polytope given only its face lattice, i.e. something like
{1}, {2}, {3}, {4},
{1, 2}, {2, 3}, {3, 4}, {4, 1},
{1, 2, 3, 4}
for a square.
Is that possible in sage?Thu, 04 Aug 2016 06:33:56 -0500http://ask.sagemath.org/question/34327/forming-a-polytope-from-only-its-combinatorial-data/Answer by Jonathan Kliem for <p>I would like to visualize a polytope given only its face lattice, i.e. something like</p>
<p>{1}, {2}, {3}, {4},
{1, 2}, {2, 3}, {3, 4}, {4, 1},
{1, 2, 3, 4}</p>
<p>for a square.</p>
<p>Is that possible in sage?</p>
http://ask.sagemath.org/question/34327/forming-a-polytope-from-only-its-combinatorial-data/?answer=47625#post-id-47625From Sage version 8.9+ there will be `CombinatorialPolyhedron`, which can be initialized with a list of facets, as
CombinatorialPolyhedron([[1,2], [2,3], [3,4], [4,1]])
With this object you have a face iterator, the face lattice and some other methods. I don't know if that helps.Tue, 27 Aug 2019 11:22:20 -0500http://ask.sagemath.org/question/34327/forming-a-polytope-from-only-its-combinatorial-data/?answer=47625#post-id-47625Answer by Saul Schleimer for <p>I would like to visualize a polytope given only its face lattice, i.e. something like</p>
<p>{1}, {2}, {3}, {4},
{1, 2}, {2, 3}, {3, 4}, {4, 1},
{1, 2, 3, 4}</p>
<p>for a square.</p>
<p>Is that possible in sage?</p>
http://ask.sagemath.org/question/34327/forming-a-polytope-from-only-its-combinatorial-data/?answer=34343#post-id-34343If by "visualize" you mean "give a geometric realization of" then I think that the answer should be "no" as I rather suspect that there are high-dimensional combinatorial polytopes that have no geometric realization. Even for three-dimensional polytopes the realization problem is delicate - there are even several layout algorithms for planar graphs. (There is at least one such implemented in sage - see:
http --- fix --- doc.sagemath.org/html/en/reference/plotting/sage/graphs/graph_plot.html
). On the other hand, if you want to see the face poset in a graphical way, this is much easier. For example see this post:
https --- fix --- sheaves.github.io/Subgroup-Lattice/
and pay attention to the "plot" method of a Poset.Fri, 05 Aug 2016 13:17:59 -0500http://ask.sagemath.org/question/34327/forming-a-polytope-from-only-its-combinatorial-data/?answer=34343#post-id-34343