What groups of symmetry are most suited for filling uniformely a spherical 3D space, whilst possessing the lowest possible surface-to-volume ratio?

Question

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.