The free-molecule drag of hard convex bodies can be written in dyadic notation in terms of two purely geometrical integrals over the closed body surface, A = integral dA and N = A(-1) integral nn dA. where n is the outward normal to the surface element dA at a given point. For sufficiently symmetric bodies, N is isotropic, and the drag is exactly proportional to the total surface area A, with a proportionality coefficient beta independent of the object's geometry and equal to the well-known value beta(s) for a sphere. This result yields effortlessly the drag for all regular and semi-regular polyhedra, previously known only for cubes. beta differs generally from beta(s) for bodies with anisotropic drag tensors; but it is a local maximum with respect to (small) arbitrary shape changes away from that of any body with an isotropic drag tensor. Hence, moderate departures from drag isotropy shift beta very slightly below beta(s), This maximum property provides a rationale for the common assumption of an approximate relation between area and drag. However, the relation involves the total surface area rather than projected areas, and leads to accurate predictions only for bodies with moderately anisotropic drag tensors. The tensorial method introduced leads also to simple results for less symmetric bodies, such as pyramids, double pyramids, parallelepipeds and axisymmetric figures. When collisions are predominantly inelastic, the ratio beta/beta(s) departs far less from unity than for elastic collisions. Similar properties are obtained for the thermophoretic force. (C) 2002 Elsevier Science Ltd. All rights reserved.