Transformation of three-dimensional shuffle patterns

Formulas are presented for the transformation of three-dimensional shuffle patterns into the two-dimensional domain. The results are applied to the transformation of the interstage patterns of three-dimensional multistage interconnection networks into their isomorphic two-dimensional patterns (and vice versa). The paper explains material in J. Giglmayr, 'Classification scheme for 3-D shuffle interconnection pattern,' (see Appl. Opt. vol.28, 3120-28, 1989) and corrects some algebraic results.