Equifacetted 3-spheres as topes of nonpolytopal matroid polytopes

Bokowski, Jürgen; Schuchert, Peter

doi:10.1007/bf02574049

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Manifolds With Small Valence1

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Cited by 8 publications

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“…T Triangulation T 2766 cannot be realized as a polytope, as explained in [BS95] and [Fri13]. It remains to show that triangulation T 2775 is not polytopal, which is what we expect to be the case.…”

Section: Manifolds With Small Valencementioning

confidence: 80%

Realizability and inscribability for simplicial polytopes via nonlinear optimization

Firsching

2017

Math. Program.

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We show that nonlinear optimization techniques can successfully be applied to realize and to inscribe matroid polytopes and simplicial spheres. Thus we obtain a complete classification of neighborly polytopes of dimension 4, 6 and 7 with 11 vertices, of neighborly 5-polytopes with 10 vertices, as well as a complete classification of simplicial 3-spheres with 10 vertices into polytopal and non-polytopal spheres. Surprisingly many of the realizable polytopes are also inscribable. * Supported by the DFG within SFB/TRR 109 "Discretization in Geometry and Dynamics"

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Section: Manifolds With Small Valencementioning

confidence: 80%