Does the shape of a tangerine (a sphere pinched at the poles) have a name?

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I have in mind a modified sphere which, if all longitudinal radii were equal, would just be a sphere however instead, each longitudinal radius has an increasingly smaller value than those of the ones before it. As a result, each longitudinal radius was closer to the centre than the last, in fact the drop in radius between two radii (r2 and r3, where r2 is closer to the equator) would be greater than the drop between the two radii before (r1 and r2, where r1 is the equatorial radius). Is that remotely understandable?

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I am not certain what you mean but it could be that you are thinking of a Spheroid or an Ellipsoid.

I hope this is of help.