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- W2016114328 abstract "The Koebe circle packing theorem states that every finite planar graph can be realized as the nerve of a packing of (non-congruent) circles in R^3. We investigate the average kissing number of finite packings of non-congruent spheres in R^3 as a first restriction on the possible nerves of such packings. We show that the supremum k of the average kissing number for all packings satisfies 12.566 ~ 666/53 <= k < 8 + 4*sqrt(3) ~ 14.928 We obtain the upper bound by a resource exhaustion argument and the upper bound by a construction involving packings of spherical caps in S^3. Our result contradicts two naive conjectures about the average kissing number: That it is unbounded, or that it is supremized by an infinite packing of congruent spheres." @default.
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- W2016114328 date "1994-01-01" @default.
- W2016114328 modified "2023-09-28" @default.
- W2016114328 title "Average kissing numbers for non-congruent sphere packings" @default.
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- W2016114328 doi "https://doi.org/10.4310/mrl.1994.v1.n3.a5" @default.
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