==> geometry/kissing.number.s <==
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
* = dimensions for which the answer is known.
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