#18442: Implement the barycentric subdivision of the boundary of a polytope
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Reporter: jipilab | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-6.8
Component: geometry | Resolution:
Keywords: polytope, | Merged in:
barycentric subdivision | Reviewers:
Authors: Jean-Philippe | Work issues:
Labbé | Commit:
Report Upstream: N/A | 996a8a4205d9f959af8e4841e39d16f66a06fe92
Branch: | Stopgaps:
public/ticket/18442 |
Dependencies: |
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Comment (by dimpase):
Replying to [comment:26 jipilab]:
> Yes. This is the definition of a polytope: a bounded polyhedron.
you might also find definitions of polyheda, as finite unions of convex
polyhedra.
That is, convexity is not always assumed.
>
> Basically the notion of polytope is subsumed in Sage by the class
Polyhedron.
>
> Theorically a polyhedron (with H representation) is always decomposed as
the sum of a polyhedral cone and a convex polytope, therefore polytopes
are considered in the class polyhedron simply where the cone is a point,
and the way to detect them is by checking compactness.
>
> The description uses polyhedron simply because polytope is more or less
absent from the nomenclature in sage apart from the database of polytopes.
>
hmm, and what do you compute then? The boundary of a polyhedron is not
convex...
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Ticket URL: <http://trac.sagemath.org/ticket/18442#comment:27>
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