Changes between Version 4 and Version 10 of Ticket #17215


Ignore:
Timestamp:
07/23/19 07:44:02 (2 years ago)
Author:
jipilab
Comment:

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  • Ticket #17215

    • Property Status changed from new to needs_work
    • Property Component changed from combinatorics to geometry
    • Property Summary changed from Bounding hyperplanes for polyhedra to Supporting cone & normal cone of faces of polyhedra
    • Property Milestone changed from sage-6.4 to sage-8.9
    • Property Keywords days100 added
  • Ticket #17215 – Description

    v4 v10  
    1 As far as I recall, a point v on a convex polyhedron P is a vertex of P if and only if there exists an affine hyperplane in the linear span of P which intersects P only in v. Knowing such a w is a good certificate for v being a vertex.
     1A point v on a convex polyhedron P is a vertex of P if and only if there exists an affine hyperplane in the linear span of P which intersects P only in v. Knowing such affine hyperplane is a good certificate for v being a vertex.
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    3 Do we have a method for finding such a w ?
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    5 I assume similar things exist for higher-dimensional faces of P rather than vertices?
     3This ticket implements the method `normal_cone` for faces of polyhedra, consisting of all the directions of the normals to supporting hyperplanes of the specified face.