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A density bound for efficient packings of 3-space with centrally symmetric convex bodies

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Edwin H. Smith
Edwin H. Smith
Affiliation:
Department MCIS, Jacksonville State University, Jacksonville, AL 36265, U.S.A.
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Abstract

It is shown that every compact convex set K which is centrally symmetric and has a non-empty interior admits a packing of Euclidean 3-space with density at least 0.46421 … The best such bound previously known is 0.30051 … due to the theorem of Minkowski-Hlawka. It is probable that there is such a lower bound which is significantly greater than the one shown in this note, since there is a packing of congruent spheres which has density

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 137 - 144
Copyright
Copyright © University College London 1999

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