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Journal of the London Mathematical Society 2003 67(1):29-40; doi:10.1112/S0024610702003873
© 2003 by London Mathematical Society
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© The London Mathematical Society

Simultaneous Packing and Covering in Three–Dimensional Euclidean Space

Chuanming Zong

School of Mathematical Sciences, Peking University Beijing 100871, China, cmzong{at}math.pku.edu.cn

Received 1 June 2001. Revision received 14 March 2002.

It is proved that the simultaneous lattice packing and lattice covering constant of every three-dimensional centrally symmetric convex body is less than or equal to 7/4. Consequently, for any three-dimensional convex body K there is a corresponding lattice packing in which no extra translate of K can be added.


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