## Abstract

A dihedral (trihedral) wedge is the intersection of two (resp. three) half-spaces in R^{3}. It is called α-fat if the angle (resp., solid angle) determined by these half-spaces is at least α > 0. If, in addition, the sum of the three face angles of a trihedral wedge is at least γ > 4π/3, then it is called (γ, α)-substantially fat. We prove that, for any fixed γ > 4π/3, α > 0, the combinatorial complexity of the union of n (a) α-fat dihedral wedges, (b) (γ, α)-substantially fat trihedral wedges is at most O(n^{2+ε}), for any ε > 0, where the constants of proportionality depend on ε, α (and γ). We obtain as a corollary that the same upper bound holds for the combinatorial complexity of the union of n (nearly) congruent cubes in R^{3}. These bounds are not far from being optimal.

Original language | English |
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Pages | 19-28 |

Number of pages | 10 |

DOIs | |

State | Published - 2001 |

Externally published | Yes |

Event | 17th Annual Symposium on Computational Geometry (SCG'01) - Medford, MA, United States Duration: 3 Jun 2001 → 5 Jun 2001 |

### Conference

Conference | 17th Annual Symposium on Computational Geometry (SCG'01) |
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Country/Territory | United States |

City | Medford, MA |

Period | 3/06/01 → 5/06/01 |