Superegg
In geometry, a superegg is a solid of revolution obtained by rotating an elongated superellipse with exponent greater than 2 around its longest axis. It is a special case of superellipsoid.
Unlike an elongated ellipsoid, an elongated superegg can stand upright on a flat surface, or on top of another superegg. This is due to its curvature being zero at the tips. The shape was popularized by Danish poet and scientist Piet [Hein (Denmark)|Piet Hein]. Supereggs of various materials, including brass, were sold as novelties or "executive toys" in the 1960s.
Mathematical description
The superegg is a superellipsoid whose horizontal cross-sections are circles. It is defined by the inequalitywhere R is the horizontal radius at the "equator", and h is one half of the height. The exponent p determines the degree of flattening at the tips and equator. Hein's choice was p = 2.5, and R/''h'' = 6/5.
The definition can be changed to have an equality rather than an inequality; this changes the superegg to being a surface of revolution rather than a solid.