# Unions of fat convex polytopes have short skeletons

Boris Aronov, Mark de Berg

Research output: Contribution to journalArticle

### Abstract

The skeleton of a polyhedral set is the union of its edges and vertices. Let P be a set of fat, convex polytopes in three dimensions with n vertices in total, and let f max be the maximum complexity of any face of a polytope in P. We prove that the total length of the skeleton of the union of the polytopes in P is at most O(α(n)· log * n · log f max) times the sum of the skeleton lengths of the individual polytopes.

Original language English (US) 53-64 12 Discrete and Computational Geometry 48 1 https://doi.org/10.1007/s00454-012-9422-8 Published - Jul 2012

### Fingerprint

Convex Polytopes
Oils and fats
Skeleton
Union
Polytopes
Polyhedral Sets
Polytope
Three-dimension
Face

### Keywords

• Combinatorial complexity
• Convex polytopes
• Fat polytopes
• Skeleton of union

### ASJC Scopus subject areas

• Theoretical Computer Science
• Computational Theory and Mathematics
• Discrete Mathematics and Combinatorics
• Geometry and Topology

### Cite this

Unions of fat convex polytopes have short skeletons. / Aronov, Boris; de Berg, Mark.

In: Discrete and Computational Geometry, Vol. 48, No. 1, 07.2012, p. 53-64.

Research output: Contribution to journalArticle

Aronov, Boris ; de Berg, Mark. / Unions of fat convex polytopes have short skeletons. In: Discrete and Computational Geometry. 2012 ; Vol. 48, No. 1. pp. 53-64.
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