A variation of a mathematical model of the structure of a pulmonary ventilatory unit is used to generate its internal ductal tree and associated alveolar architecture. The model unit comprises a space-filling block of regular polyhedra; ducts and alveoli were formed by opening specific common faces between polyhedra. The model employs a physically reasonable optimization strategy of maximizing gas exchange while minimizing the mean transit time to ventilate the ventilatory unit (assumed to be proportional to the mean path length) in order to create the ductal tree. The sensitivity of the global architecture to the competitive optimization parameters used and the tree structure are compared with independently published measurements. The study concludes that it is possible to model the detailed architecture of a unit using a simple space-invariant uniform modular structure for both alveoli and ductal parts. The close similarity between model and experimental measurement strongly suggests that the optimization used to create the unit is a likely one from a functional biological standpoint. The insensitivity of the architecture to the competition between the optimization parameters supports the belief that it is not important to consider the detailed measured size distribution of alveoli when considering how the large structure of the ventilatory unit is built up.