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This is surprising, but less surprising when you realise it is rotating about one of the foci, not the centre.
That page didn't have a formula, in either cartesian or polar coordinates, for the shape of the object. Lots of formulas, but I didn't see anything I could use to create a 3d mesh and print one of these things out on my printer.
Relevant to this is the J2 Perturbation [1], commonly used when accurately modeling the Earth as an oblate spheroid (like in the article image, but less drastic) rather than a perfect sphere. This has resultant effects on orbits, such as the "gravity wells" in the GEO belt at 105degW and 75degE. There are higher-order perturbations [2] as you closer approximate the Earth's actual shape, such as J3, J4, etc.

[1] https://ai-solutions.com/_freeflyeruniversityguide/j2_pertur...

[2] https://oer.pressbooks.pub/lynnanegeorge/chapter/chapter-10-...