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August 28th, 2017, 04:46 PM   #1
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Ulam's packing conjecture with spheres

“(Packed) identical balls must leave (a maximum of) ~25.95% of the space empty." [Wikipedia]

Is there a maximum curvature for the average, asymmetric packing of spheres in 3D space?

In the 2D case, maximally packed circles can go on countlessly with zero curvature in six directions.
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October 2nd, 2017, 12:08 PM   #2
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What symmetry group does the densest packing of equal spheres belong to?
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