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Then a packing of unit balls in ${\\Bbb R}^3$ consisting of translates of $L$ has a density at most $\\pi /(3d\\sqrt{3-d^2})$, with equality for a certain lattice packing of unit balls. Let $L \\subset {\\Bbb R}^4$ be the union of unit balls, whose centres lie on the $x_3x_4$ coordinate plane, and form either a square lattice or a regular triangular lattice, of edge length $2$. 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