Non-Realizable Minimal Vertex Triangulations of Surfaces: Showing Non-Realizability using Oriented Matroids and Satisfiability Solvers

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dc.creatorSchewe, Lars
dc.date2008-01-16
dc.date.accessioned2026-07-07T08:54:56Z
dc.date.available2026-07-07T08:54:56Z
dc.descriptionWe show that no minimal vertex triangulation of a closed, connected, orientable 2-manifold of genus 6 admits a polyhedral embedding in R^3. We also provide examples of minimal vertex triangulations of closed, connected, orientable 2-manifolds of genus 5 that do not admit any polyhedral embeddings. We construct a new infinite family of non-realizable triangulations of surfaces. These results were achieved by transforming the problem of finding suitable oriented matroids into a satisfiability problem. This method can be applied to other geometric realizability problems, e.g. for face lattices of polytopes.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0801.2582
dc.identifierhttp://arxiv.org/abs/0801.2582
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/146120
dc.subjectMetric Geometry
dc.subjectCombinatorics
dc.subject52B70; 52C40
dc.titleNon-Realizable Minimal Vertex Triangulations of Surfaces: Showing Non-Realizability using Oriented Matroids and Satisfiability Solvers
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