Theories of abnormal grain growth (AGG) in three dimensions usually approximate an abnormal grain by a sphere. The abnormal grain is then represented by its spherical equivalent grain radius. This study, by contrast, treats AGG in terms of concepts that include both the boundary curvature and the number of faces of the abnormal grain. We treat AGG for the case of pinned matrices, including the phenomena of initiation and growth kinetics. The influence of interfacial energy and mobility of the abnormal grain boundary are also discussed.