Discrete & Computational Geometry

, Volume 13, Issue 3, pp 477–515

Largestj-simplices inn-polytopes

  • P. Gritzmann
  • V. Klee
  • D. Larman

DOI: 10.1007/BF02574058

Cite this article as:
Gritzmann, P., Klee, V. & Larman, D. Discrete Comput Geom (1995) 13: 477. doi:10.1007/BF02574058


Relative to a given convex bodyC, aj-simplexS inC islargest if it has maximum volume (j-measure) among allj-simplices contained inC, andS isstable (resp.rigid) if vol(S)≥vol(S′) (resp. vol(S)>vol(S′)) for eachj-simplexS′ that is obtained fromS by moving a single vertex ofS to a new position inC. This paper contains a variety of qualitative results that are related to the problems of finding a largest, a stable, or a rigidj-simplex in a givenn-dimensional convex body or convex polytope. In particular, the computational complexity of these problems is studied both for
-polytopes (presented as the convex hull of a finite set of points) and for-polytopes (presented as an intersection of finitely many half-spaces).

Copyright information

© Springer-Verlag New York Inc. 1995

Authors and Affiliations

  • P. Gritzmann
    • 1
  • V. Klee
    • 2
  • D. Larman
    • 3
  1. 1.Fb. IV, MathematikUniversität TrierTrierGermany
  2. 2.Department of Mathematics, GN-50University of WashingtonSeattleUSA
  3. 3.Department of MathematicsUniversity CollegeEngland

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