Regular simplices and Gaussian samples

Yuliy M. Baryshnikov, Richard A. Vitale

Research output: Contribution to journalArticlepeer-review

41 Citations (Scopus)


We show that if a suitable type of simplex in R n is randomly rotated and its vertices projected onto a fixed subspace, they are as a point set affine-equivalent to a Gaussian sample in that subspace. Consequently, affine-invariant statistics behave the same for both mechanisms. In particular, the facet behavior for the convex hull is the same, as observed by Affentranger and Schneider; other results of theirs are translated into new results for the convex hulls of Gaussian samples. We show conversely that the conditions on the vertices of the simplex are necessary for this equivalence. Similar results hold for random orthogonal transformations.

Original languageEnglish
Pages (from-to)141-147
Number of pages7
JournalDiscrete & Computational Geometry
Issue number1
Publication statusPublished - Dec 1 1994
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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