superellipsoid

right|400px|thumb|Superellipsoid collection with exponent parameters, created using POV-Ray. Here, e = 2/r, and n = 2/t (equivalently, r = 2/e and t = 2/n).

In mathematics, a superellipsoid (or super-ellipsoid) is a solid whose horizontal sections are superellipses (Lamé curves) with the same squareness parameter \epsilon_2, and whose vertical sections through the center are superellipses with the squareness parameter \epsilon_1. It is a generalization of an ellipsoid, which is a special case when \epsilon_1=\epsilon_2=1.