Partitions of a Polytope and Mappings of a Point Set to Facets
نویسنده
چکیده
Three theorems of this paper generalize previous results of the author on conjectures of A. Bezdek and V. V. Proizvolov. They show the existence of mappings from a given point set to the set of facets of a given polytope that satistfy some special conditions. Developing the same technique, some results on convex polytope partitions are presented, two of them dealing with partitions with prescribed measures of parts. Then we prove a corollary on existence of a possibly non-convex polytope with given set of vertices, containing given points in its interior. We also consider problems of the following type: find an assignment of vectors from a given set to the parts of a given convex partition of Rn so that the shifts of the parts by their corresponding vectors either do not intersect by interior points or cover Rn.
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عنوان ژورنال:
- Discrete & Computational Geometry
دوره 34 شماره
صفحات -
تاریخ انتشار 2005