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of upper densities obtained by packings that are subcollections of the supply collection. If the supply collection consists of convex bodies of bounded diameter, there exists a packing whose packing density is equal to the packing constant, and this packing constant does not vary if the balls in the
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of the above respectively. If the density exists, the upper and lower densities are equal. Provided that any ball of the
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One is often interested in packings restricted to use elements of a certain supply collection. For example, the supply collection may be the set of all balls of a given radius. The
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of the space filled by the figures making up the packing. In simplest terms, this is the ratio of the volume of bodies in a space to the volume of the space itself. In
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of a fixed body is also a common supply collection of interest, and it defines the translative packing constant of that body.
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and their interiors pairwise do not intersect, then the collection is a packing in
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Groemer, H. (1986), "Some basic properties of packing and covering constants",
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states that 3-balls have the lowest packing constant of any convex solid. All
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definition of density are replaced by dilations of some other convex body.
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