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August 28th, 2017, 03:46 PM  #1 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 401 Thanks: 27 Math Focus: Number theory  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. 
October 2nd, 2017, 11:08 AM  #2 
Senior Member Joined: May 2015 From: Arlington, VA Posts: 401 Thanks: 27 Math Focus: Number theory 
What symmetry group does the densest packing of equal spheres belong to?


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conjecture, packing, spheres, ulam 
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