A series of two articles discusses possible morphol. evidence for oligomerization of growth units in the crystn. of tetragonal lysozyme, based on a rigorous graph-theoretic derivation of the F faces.  In the first study (Part I), the growth layers are derived as valid networks satisfying the conditions of F slices in the context of the PBC theory using the graph-theoretic method implemented in program FFACE [C.S. Strom, Z. Krist. 172 (1985) 11].  The anal. is performed in monomeric and alternative tetrameric and octameric formulations of the unit cell, assuming tetramer formation according to the strongest bonds.  F (flat) slices with thickness Rdhkl (1/2) are predicted theor. in the forms {110}, {011}, {111}.  The relevant energies are established in the broken bond model.  The relation between possible oligomeric specifications of the unit cell and combinatorially feasible F slice compns. in these orientations is explored.