## Abstract

Relative to a given convex body C, a j-simplex S in C is largest if it has maximum volume (j-measure) among all j-simplices contained in C, and S is stable (resp. rigid) if vol(S)≥vol(S′) (resp. vol(S)>vol(S′)) for each j-simplex S′ that is obtained from S by moving a single vertex of S to a new position in C. This paper contains a variety of qualitative results that are related to the problems of finding a largest, a stable, or a rigid j-simplex in a given n-dimensional convex body or convex polytope. In particular, the computational complexity of these problems is studied both for[Figure not available: see fulltext.]-polytopes (presented as the convex hull of a finite set of points) and for ℋ-polytopes (presented as an intersection of finitely many half-spaces).

Original language | English |
---|---|

Pages (from-to) | 477-515 |

Number of pages | 39 |

Journal | Discrete and Computational Geometry |

Volume | 13 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1995 |

Externally published | Yes |