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SIMULTANEOUS PACKING AND COVERING IN THREE–DIMENSIONAL EUCLIDEAN SPACE

Published online by Cambridge University Press:  25 March 2003

CHUANMING ZONG
CHUANMING ZONG
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, Chinacmzong@math.pku.edu.cn
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Abstract

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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 67 , Issue 1 , February 2003 , pp. 29 - 40
Copyright
The London Mathematical Society, 2003

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