Onsagerian formula for the excluded volume of spherodisks

By a formal analytic argument based on Minkowski’s expression for the isotropic average of the excluded
volume of convex bodies,we reproduce the exact formula for the excluded volume of two spherorods—also known
by the more traditional name of spherocylinders, which is classically derived through a geometric construction.
By applying the same argument to spherodisks, which represent discotic platelets, we obtain a simple explicit
formula for their excluded volume, whose validity is corroborated by a shape-reconstruction algorithm.