Explicit excluded volume of cylindrically symmetric convex bodies

We represent explicitly the excluded volume V-e{B-1, B-2} of two generic cylindrically symmetric, convex rigid bodies, B-1 and B-2, in terms of a family of shape functionals evaluated separately on B-1 and B-2. We show that V-e{B-1, B-2} fails systematically to feature a dipolar component, thus making illusory the assignment of any shape dipole to a tapered body in this class. The method proposed here is applied to cones and validated by a shape-reconstruction algorithm. It is further applied to spheroids (ellipsoids of revolution), for which it shows how some analytic estimates already regarded as classics should indeed be emended.