Hard superball model

The shape of superballs interpolates between octahedra (q = 0.5) and cubes (q = ∞) via spheres (q = 1).

A superball is defined by the inequality

$\left|{\frac {x}{a}}\right|^{2q}+\left|{\frac {y}{a}}\right|^{2q}+\left|{\frac {z}{a}}\right|^{2q}\leq 1$

where x, y and z are scaled Cartesian coordinates with q the deformation parameter and radius a. The shape of the superball interpolates smoothly between two Platonic solids, namely the octahedron (q = 0.5) and the cube (q = ∞) via the sphere (q = 1) as shown in the left figure.