[seqfan] Higher dimensional analogues to plane division by ellipses?

[Jess Tauber]

OEIS A051890 relates to the maximal number of regions into which ellipsoids may divide the plane. A014206 for division of the plane by circles.

I've seen BOTH these sequences with regard to the combinatorics of nucleons in real nuclei.

All sorts of questions come to mind, but I'll limit myself to these:

Firstly, are there analogous sequences for higher dimensional analogues, say, volume elements in a larger volume cut by ellipsoids or spheres, and are the formulae regularly relatable to those of the plane?

Secondly, what if we consider other conic sections (and higher analogues), either uniformly or in combination?

I tried looking up volume division at the Wolfram site, no luck.

Thanks.

Jess Tauber
goldenratio at earthlink.net