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The analytical algebraic method developed for the selection of active slip systems in the case of glide on {110} (111) systems [Royer, Mohr & Tavard, J. Appl. Cryst. (1978). 11, 35-39] is extended to (111) pencil glide. This approach leads to an algebraic determination of all amounts of glide and corresponding slip plane orientations in both cases of effective slip on three or four systems. Numerical applications have led to a reduction of computer time by a factor of 10-3 with respect to previous investigations.