We have investigated the self-assembly of a strong dipolar molecule (LDipCC) on the semiconducting Si(111)-B surface with scanning tunneling microscopy (STM), density functional theory (DFT) calculations and STM simulations. Although the formation of an extended two-dimensional network was clearly revealed by STM under ultra-high vacuum, the assignment of a specific STM signature to the different terminal groups from the LDipCC molecular unit required a complete analysis by numerical simulations. The overall observed assembly is explained in terms of STM contrasts associated with the molecular structure of LDipCC and the molecule-surface interactions. To distinguish the relative arrangement of the dipolar molecules within the assembly, a rational combination of experimental results and electronic structure calculations allows us to identify a single adsorbed LDipCC phase in which the molecular dipoles are homogeneously arranged into a parallel fashion on the Si(111)-B surface.