In this paper graphical constructions are given for the solution of the following problems:—

Given the gnomonic or stereographic projections of the poles of four faces, find the projection of the pole of any other face.

Given the gnomonic or stereographic projections of the poles of a crystal, find the projections of the poles of a twin-crystal.

Given the projection of two zones, find the angle between them.

Given the gnomonic projection of the poles of a crystal, find the orthographic projections of its edges, etc.