Geometric characterizations of centroids of simplices

Steven G. Krantz, John E. McCarthy, Harold R. Parks

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


We study the centroid of a simplex in space. Primary attention is paid to the relationships among the centroids of the different k-skeletons of a simplex in n-dimensional space. We prove that the 0-dimensional skeleton and the n-dimensional skeleton always have the same centroid. The centroids of the other skeleta are generically different (as we prove), but there are remarkable instances where they coincide in pairs. They never coincide in triples for regular pyramids.

Original languageEnglish
Pages (from-to)87-109
Number of pages23
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Apr 1 2006


  • Centroid
  • Dynamics
  • Polytope
  • Pyramid
  • Rigid body
  • Simplex


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