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Is there an abstraction of a leminscate/consonant with 3+ center points?

Yes, the Lissajous https://en.wikipedia.org/wiki/Lissajous_curve which also can be turned vertical (to look like an 8 instead of ∞).

But this doesnt have the property that the product of the distances to the focal points is constant no?

Heres two examples for 3 and 6 points in 2D, 3D respectively: https://en.wikipedia.org/wiki/Cassini_oval#Generalizations

These are symmetric as well though.

Kinda looking like hydrogen orbitals.