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.