The volumes of simplices, or, find the penguin

Fima C. Klebaner, Aidan Sudbury, G. A. Watterson

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3 Citations (Scopus)


Given the equations for the n + 1 hyperplanes that bound an n-simplex in Rn, simple formulae are derived for the contents of the n — r simplices (0 ≤ r ≤ n) embedded in it. For example, when n = 3, the formulae include the volume of the tetrahedron, the areas of its faces and the lengths of its edges. 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 14 N 99.

Original languageEnglish
Pages (from-to)263-268
Number of pages6
JournalJournal of the Australian Mathematical Society
Issue number2
Publication statusPublished - 1 Jan 1989


  • simplex
  • volume

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