Results are presented of friction and wear measurements during diamond polishing using new instrumentation designed and built in our laboratory. The wear rates are found to be highly anisotropic, depending both on the crystallographic plane and on the direction along which sliding occurs. Friction measurements performed during polishing on a {100} plane in the [100] direction (the direction of the highest wear rate on the plane) and the [110] direction (the direction of the lowest wear rate) exhibit similar trends to those occurring in friction at low speed on the {100} face, with the [100] direction having a higher friction coefficient than the [110] direction. It was further found that the variation of friction with pressure in the [100] and the [110] directions are different, pointing to the fact that two wear mechanisms operate in the two principal directions. The results are consistent with, and provide macroscopic evidence in support of, a model of mechanically induced transformation of diamond to sp(2) hybridized carbon occurring on the diamond surface during polishing along the direction in which the wear rate is high. In contrast to this, the wear process proposed for the [110] direction is one of micro-fracture, in agreement with earlier studies of the polished surface and the wear debris. By explaining the wear mechanism in terms of two different types of processes operating in the two directions, we are able to understand the high anisotropy observed.