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The egg shape drawn here is completely phenomenological.

Ideally one would like to derive the egg shape from first principles. This way the appearance of numerical factors, like 1.3 and 0.2, would be explained. Possibly a derivation of the egg shape from first principles will reveal better values for those numerical factors, e.g., values that are related to universal constants like π, e, φ, γ,...

It should be straightforward to generalize the construction into three dimensions. PRs are very welcome!