It is shown that a packing of unit spheres in three-dimensional Euclidean space can have density at most 0.773055..., and that a Voronoi polyhedron defined by such a packing must have volume at least 5.41848... These bounds are superior to the best bounds previously published  (0.77836 and 5.382, respectively), but are inferior to the tight bounds of 0.7404... and 5.550... claimed by Hsiang .
Our bounds are proved by cutting a Voronoi polyhedron into cones, one for each of its faces. A lower bound is established on the volume of each cone as a function of its solid angle. Convexity arguments then show that the sum of all the cone volume bounds is minimized when there are 13 faces each of solid angle 4π/13.
Unit Sphere Local Density Solid Angle Outer Radius Discrete Comput Geom
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