volume 30, issue 1, P133-160 2003
DOI: 10.1007/s00454-003-2928-3
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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, and (b) (γ , α)-substantially fat trihedral wedges is at most…

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