Nonrealizable minimal triangulations of surfaces

Schewe L (2006)


Publication Type: Conference contribution

Publication year: 2006

Series: Oberwolfach Reports

Book Volume: 3

Pages Range: 707-708

Conference Proceedings Title: Discrete Differential Geometry: Abstracts from the workshop

Journal Issue: 1

Abstract

We show that no minimal vertex triangulation of a closed, connected, orientable 2-manifold of genus 6 admits a polyhedral embedding in R3. 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 triangula tions 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.

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How to cite

APA:

Schewe, L. (2006). Nonrealizable minimal triangulations of surfaces. In Discrete Differential Geometry: Abstracts from the workshop (pp. 707-708).

MLA:

Schewe, Lars. "Nonrealizable minimal triangulations of surfaces." Proceedings of the Discrete Differential Geometry: Abstracts from the workshop 2006. 707-708.

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