This paper discusses how polyhedron interpretation techniques are simplified if the objects are rectangular trihedral polyhedra. This restriction enables one to compute the spatial orientation of a given corner and its motion from its image in terms of polar coordinates, Eulerian angles, and quaternions. One can also interpret the shape and the face adjacency from local information only. The necessary constraints are listed, and some examples are given to compare the presented scheme to existing ones. The possible nonuniqueness of the interpretation is also discussed.