From the Feb. 1992 issue of Scientific American

Kissing Numbers

Dimension Lower limit Upper limit

1* 2 2 2* 6 6 3* 12 12 4 24 25 5 40 46 6 72 82 7 126 140 8* 240 240 9 306 380

10 500 595 11 582 915 12 840 1,416 13 1,130 2,233 14 1,582 3,492 15 2,564 5,431 16 4,320 8,313 17 5,346 12,215 18 7,398 17,877 19 10,688 25,901 20 17,400 37,974 21 27,720 56,852 22 49,896 86,537 23 93,150 128,096 24* 196,560 196,560

REFERENCES (from the Sci. Am. article)

The Problem of the Thirteen Spheres. John Leech in Mathematical Gazette, Vol. 40, No. 331, pages 22-23; February 1956

Sphere Packings, Lattics and Groups. John Horton Conway and Neil J. A. Sloane. Springer-Verlag, 1988.

Sphere Packings and Spherical Geometry--Kepler's Conjecture and Beyond, preprint. Wu-Yi Hsiang. Center for Pure and Applied Mathematics, University of California, Berkeley, July 1991.

-- David Radcliffe radcliff@csd4.csd.uwm.edu

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