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I am looking for the closest known approximate solution to Kelvin foams problem that would obey a spherical symmetry.

One alternative way of formulating it: I am looking for an equivalent of Weaire–Phelan structure that would be able to fill in a sphere, while stacked in layers around the central core.

Another alternative way of formulating it: I am looking for a crystalline structure that would result in growth of spherical or (almost) spherical crystals.

In case it is impossible, what would be the closest quasicristaline structure for this? Any pointers towards textbooks or publications or just intuitive explanations would be more then welcome.

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    $\begingroup$ my idea would be to try to find such a packing for the platonic solids first and then modify the solution in a way that turns edges of the solid into geodesic arcs on its containing sphere. For a cube that is sometimes done to obtain the so-called "cubed sphere", which in turn is used to define space filling curves on the sphere. $\endgroup$ Dec 31, 2013 at 15:42
  • $\begingroup$ Thanks, I am currently trying to do this with a computational algorithm. However I hoped that there would be a mathematical object that have already been explored that could fit my needs. $\endgroup$ Dec 31, 2013 at 17:15
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    $\begingroup$ Stupid question: are you restricted to Euclidean spaces? If not, hyperbolic spaces could yield such a sphere packing in the spirit of Escher's circle limit, but I'm no expert in that respect. $\endgroup$ Jan 2, 2014 at 11:29
  • $\begingroup$ Yes, I am restricted to Euclidean space, but thanks for the pointer: it is an interesting set of ideas I wasn't aware of before. $\endgroup$ Jan 2, 2014 at 16:33
  • $\begingroup$ I do not understand what you are looking for; it would help if you edited your question to be more precise with your terms. For instance, what do you mean by "obey a spherical symmetry"? It is also unclear to me what would be considered "equivalent of Weaire-Phelan", nor what "layers around the central core" refers to. In the next alternative, you make reference to "growth" -- what model for growth are you interested in? $\endgroup$
    – j.c.
    Jan 20, 2014 at 18:34

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