All the cells that compose the primary body of roots and shoots of plants derive from one or a few structural initial cells located within their apices. These cells are polyhedra, the number of whose wall faces (or sides) have increased during evolution. Mosses, algae, and leptosporangiate ferns may have initial cells with two, three or four faces, initial cells of eusporangiate ferns have five or six faces, while those of gymnosperms and angiosperms have eight faces. Seven-sided initial cells seem to be rare or absent. A scheme is proposed whereby the number of faces of an initial cell increases through an altered type of division and a suggestion is made as to how such changes may be fixed during ontogeny and, hence, how initial cell complexity becomes an aspect of plant phylogeny. In many "lower" plants, the orientation of cytokinesis in the structural initials is strictly regulated so that most, or all, of the faces of the mother cell wall pass into a daughter cell (merophyte) in a particular sequence. The same may also apply in "higher" plants, though from observational evidence this is less certain, but is nevertheless theoretically plausible. The division sequence may also be accompanied by a corresponding sequence of nuclear rotations which allows the chromosomes in the post-mitotic nucleus to retain the same positions, relative to the faces of the mother cell, that they had occupied prior to mitosis. Nuclear rotation may also facilitate conservative DNA segregation at mitosis in a structural initial, but, although there is some evidence for this, it is not an obligatory condition. Calculations are made, using three sets of conditions for division and DNA segregation, of the minimum angle of nuclear rotation necessary to accomplish one complete cycle of oriented divisions which involve all the faces of an initial (mother) cell, where the number of faces ranges from three to eight. The corresponding sequences of face involvements are also presented. Some sequences are unique to a given set of conditions. These can be compared with known sequences of divisions. In a case of a six-sided initial cell of a fern, the predicted and observed sequences correspond with semi-conservative DNA segregation and with a division rule whereby the oldest face of the mother cell wall is the one that will be donated to the next daughter merophyte. Many of the processes proposed that accompany and maintain initial cell structure and division are amenable to experimental testing.