The surface area of an ellipsoid of revolution is well-known [43]. Normalized by the surface area of a sphere with equal volume, the surface area A becomes:
The surface area of a triaxial ellipsoid involves a more complicated closed form involving elliptic functions [44,45]. It is a classical result from mathematical antiquity that of all objects of a given volume, the sphere has the minimum surface area and that in 2-D, of all regions of finite area, the circle has the minimum perimeter [40]. Such inequalities for general shape functionals have then come to be called "isoperimetric." The reciprocal of the quantities defined in eq. (2-3) are also widely known as the "sphericity" of a particle [46,47,48].