In this work, a numerical boundary element algorithm is described that can be applied. to particles of arbitrary shape that are modeled as arrays of fat triangular plates. It is general enough to accommodate stick or slip boundary conditions as well as the presence of external forces on the surrounding fluid. The algorithm is used in the present work to study the transport: of axisymmetric particles in the absence of external forces. Specifically, translational and rotational diffusion constants as well as the viscosity coefficient of ellipsoids (prolate and oblate), short rods, and toroids subject to stick and slip boundary conditions are reported. The transport properties of the corresponding "smooth" particles are estimated by carrying out numerical studies of several model structures and extrapolating to the limit of a model in which the number of plates goes to infinity. This is called the extrapolated shell model. Many of the transport properties are being reported for the first time. In cases where the transport properties are already known, the boundary element-extrapolated shell calculations are accurate to within a few percent.