Illustrating Kepler's Conjecture on Sphere Packing

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The ratio of the volume of a sphere to that of a rhombic dodecahedron (RD) is 0.74048…, corresponding to the volume fraction for sphere packing in Kepler's conjecture. Since the attached RDs fill space, this ratio is valid for any number of RDs and their inscribed spheres.

Contributed by: Sándor Kabai (November 2016)
Open content licensed under CC BY-NC-SA


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Thomas Hales published a proof of the conjecture in 2005, involving computer analysis of thousands of sphere-packing arrangements.



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