>It’s not clear why the superellipse would be common and the superhyperbola obscure, but here’s some speculation. First of all, the superellipse had an advocate, Piet Hein. If the superhyperbola has an advocate, he’s not a very effective advocate.<p>Piet Hein was a designer. The superellipse, being closed, is a much more useful shape for designing physical objects, and fitting a roundish shape into a rectangular space is a useful property in our world of architectural square corners.