Nonrealizable Minimal Vertex Triangulations of Surfaces: Showing Nonrealizability Using Oriented Matroids and Satisfiability Solvers

@article{Schewe2010NonrealizableMV,
  title={Nonrealizable Minimal Vertex Triangulations of Surfaces: Showing Nonrealizability Using Oriented Matroids and Satisfiability Solvers},
  author={Lars Schewe},
  journal={Discrete & Computational Geometry},
  year={2010},
  volume={43},
  pages={289-302}
}
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. Correcting a previous error in the literature, we construct the first infinite family of such nonrealizable triangulations of surfaces. These results were achieved by transforming the problem of… CONTINUE READING