Polytypism in III-V semiconductor nanowires is a topic that has received considerable attention in recent years. Achieving a pure nanowire crystal phase requires well-controlled and advanced parameter tuning for most III-V materials. Additionally, the new and unusual phases sometimes observed may present unique material properties if they can be controllably fabricated. With the prospect of using nanowires in applications within several different fields (including electronics, photonics, and life science), theoretical models are necessary to explain experimental trends and to attain a high level of crystal phase control. At present, there is no theoretical model (or combination of models) that fully explains how and why nanowire crystal structures commonly include several different polytypes. Here we use combinatorics and interlayer interactions to include higher order polytypes (4H and 6H) with the aim to explain nanowire crystal structure beyond the well-investigated zinc blende-wurtzite polytypism. Predictions from our theoretical models compare well with experimental results.