Three-dimensional imagery is rapidly transforming the reconstruction, visualization and conceptualization of ancient monuments. We report (and reflect on the value of) digital reconstruction of a third-millennium BC megalithic tower and surrounding landscape using a combination of architectural drawing, 3D photogrammetry and geographic information systems (GIS) mapping. Our results indicate that at least 181 metric tons of limestone (mean boulder weight 386kg) were hewn to create a monument 20m in diameter and at least 4m high. In addition to considering possible practical functions, including water extraction and a potential defensive purpose, we argue that this tower's central significance lay in its monumentality. At least sixty comparable Umm an-Nar period towers are known; and, as much as the model itself, the process of planning and executing a 3D model led us to recognize that a community of skilled builder/architects used a sophisticated mental template (with variation on a theme) to design and construct them.