Using a unique one-pot convergent anionic polymerization strategy, 18 (polystyrene)(star)-b-(polyisoprene)(linear)-b-(polystyrene)(star) (SnISn) pom-pom triblock copolymers were synthesized varying a range of architectural parameters including PS arm molecular weight (M-n,M-star), the number of arms contained in the star (n), and the PI midblock molecular weight (M-n,M-PI). A selected series of five of these 18, in which M-n,M-star was held approximately constant between 14.3 and 16.5 kDa, but with the numbers of arms in the star and PI midblock molecular weight varied, were selected for detailed characterization using rheology, AFM, and SAXS. The five selected all shared PS as the minority component, with star volume fractions (f(ps)) varying between 0.11 and 0.22. All samples showed clear phase separation, with three of the five adopting a highly ordered hexagonal packing of cylinders (HPC) confirmed through SAXS and AFM. The remaining two systems were limited to liquid-like packing of cylindrical domains (LLP). Longer midblock molecular weights and increased numbers of arms in the star both showed a propensity to hinder formation of a highly ordered hexagonal lattice. Increasing the number of arms in the star also favored transitions to a disordered phase at lower temperatures when overall SnISn molecular weight was held constant. The behavioral trends identified suggest interfacial packing frustration plays a prominent role in determining the ability of the system to develop highly ordered periodic structures. The chain crowding produced by the PS star architecture intrinsically favors interfacial curvature toward the majority PI component, contrary to that intrinsically favored by the block composition alone. In the two systems in which the frustration was architecturally most severe (largest n of 7.1, highest M-n,M-PI of 191 kDa), evolution of a hexagonal lattice could not be induced, even after significant thermal annealing. The pom-pom architecture itself also appears to have a significant impact on entanglement relaxation dynamics, with development of HPC morphologies only possible at elevated temperatures.