The genetic regulatory networks responsible for cell differentiation and cell cycle control can be modeled by Boolean logic networks of varying connectivity, in which each node in the network represents a gene. We describe the underlying motivation for these models, and propose a new method for categorizing the strategy functions assigned to each node based on symmetry properties of Ising hypercubes. Under biologically relevant conditions, interactions between nodes strongly restrict the available phase space of the network, implying that the experimentally observed conservation of wild-type phenotype may arise automatically due to the combinatoric properties of the underlying genetic network.