On triangulations of the convex hull ofn points

Abstract

A setS ofn points in Euclideand-space determines a convex hull which can be triangulated into some numberm of simplices using the points ofS as vertices. We characterize those setsS for which all triangulations minimizem. This is used to characterize sets of points maximizing the volume of the smallest non-trivial simplex.

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Dedicated to Paul Erdős on his seventieth birthday

This work was supported in part by NSF Grants MCS 81-02519 and MCS 82-03347.

This work supported in part by NSF Grants MCS 81-02519 and MCS 82-03347

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Rotschild, B.L., Straus, E.G. On triangulations of the convex hull ofn points. Combinatorica 5, 167–179 (1985). https://doi.org/10.1007/BF02579380

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AMS subject classification (1980)

  • 51 M 05
  • 52 A 20