In previous models of the building behaviour of termites, physical and logistic constraints that limit the movement of termites andpheromones have been neglected. Here, we present an individual-based mo del of termite construction that includes idealized constraints on the diffusion of pheromones, the movement of termites, and the integrity of the architecture that they construct. The model allows us to explore the extent to which the results of previous idealized models (typically realised in one or two dimensions via a set of coupled partial differential equations) generalize to a physical, 3-D environment. Moreover we are able to investigate new processes and architectures that rely upon these features. We explore the role of stigmergic recruitment in pillar formation, wall building, and the construction of royal chambers, tunnels and intersections. In addition, for the first time, we demonstrate the way in which the physicality of partially built structures can help termites to achieve efficient tunnel structures and to establish and maintain entrances in royal chambers. As such we show that, in at least some cases, logistic constraints can be important or even necessary in order for termites to achieve efficient, effective constructions.