Superegg

A superegg is a solid described by the equation

$$\left\vert{\sqrt{x^2+y^2\over a^2}\,}\right\vert^n+\left\vert{z\over b}\right\vert^n=1.$$

Supereggs will balance on either end for any $a$, $b$, and $n$.

See also Egg, Superellipse

References

Gardner, M. ``Piet Hein's Superellipse.'' Ch. 18 in Mathematical Carnival: A New Round-Up of Tantalizers and Puzzles from Scientific American. New York: Vintage, 1977.