This figure shows an ellipsoid. It is definitely not a surface of rotation; indeed all three axes have different lengths. Specifically, the ratios of the lengths of the three axes (long:medium:short) are 1:^{2}⁄_{3}:^{4}⁄_{9}. The equation of this ellipsoid is: x² + 2.25y² + 5.0625z² = 1.
Each of the black lines traced along the center of a yellow stripe is the
intersection of the surface with one of the coordinate planes. Each of
those curves is an ellipse, as are all nontrivial planar crosssections of the
ellipsoid.

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I made the figure on this page by substituting my own data in a Geometry Center webpage.
Prof. Joel Roberts
School of Mathematics
University of Minnesota
Minneapolis, MN 55455
USA
Office: 351 Vincent Hall
Phone: (612) 6251076
Dept. FAX: (612) 6262017
email: roberts@math.umn.edu
http://www.math.umn.edu/~roberts