THE PRESENT PAPER ends a series of three papers devoted to the micro-mechanical conditions which render possible the appearance of shear bands in crystalline materials. It presents the results on the edges of dimension 1 (encompassing the states of the deviatoric stress applied between two vertices of the Bishop and Hill polyhedron). They show that bifurcation is possible with a relatively small number of active slip systems, in conditions of strain hardening which are of the same order of magnitude as those at the vertices. An application is given to the case of the C {112} <11-1> oriented single crystal compressed in a channel die. The characteristic experimental feature: appearance of two successive sets of bands (111) [11-2] and (11-1) [112] is explained in terms of the most favoured bifurcation planes and the local rotation of the crystal. Though convincing to predict the onset of shear bands, the above calculations do not provide a description of their intergranular development, especially crossing of the grain boundaries, since at this stage the material has been too much affected by the intense shearing to be treated by a method of bifurcation.