A complex geographical edge finishing system includes a fixture that holds an external part having a complex three-dimensional edge, a track disposed around the fixture and surrounding the edge of the part held in the fixture, and one or more finishing apparatuses that can sand, polish, buff, paint and/or apply coatings to the complex three-dimensional edge. The finishing apparatuses move about the track such that the three-dimensional edge of the part can be polished. The path of the track can substantially match, mimic or otherwise correspond to the path of the three-dimensional edge, such that special requirements for the finishing apparatuses are not required.