The neocortex makes up over 80% of the mammalian brain and is responsible for higher cognitive functions, processing of sensory inputs and orchestration of complex motor outputs. It is a 6-layered structure composed of billions of morphologically and electrically diverse neurons. Functionally, the basic unit is the neocortical column (NCC), a vertical structure of 0.5 mm wide, repeated millions of times across the neocortex and connected in an intricate but consistent way. In this thesis I investigated the role of morphologies (neurogeometry) in shaping the elaborate connectivity scheme within a column. First, I suggest a morphological basis for the higher than expected reciprocal connectivity reported experimentally between connected pairs, using a newly defined measure: the Reciprocity Index (RI), which arises from a purely mathematical concept and can be derived from the morphometric statistics of neurons. Second, I show that most experimentally reported synaptic patterns between different classes of neurons can be directly computed from the statistics of their morphologies, while some pathways would require additional functional mechanisms to refine an even more specific synaptic pattern. My thesis is done within the Blue Brain Project, the first comprehensive attempt to reverse-engineer the mammalian brain, starting with the somatosensory NCC of a P14 rat. I present in this thesis my contribution in constructing the framework for building biologically accurate circuitry. I explain how we start from 3D neuron morphologies obtained in vitro, repair them for slicing artefacts, build circuits and accurately detect potential synapses. I also explore how modelling of the experimental procedures can help us characterize biases and predict in vivo data from in vitro data. I finally present recent exploratory work on how to use the supercomputing power to design novel in silico protocols to investigate the emergent dynamics of the neocortical column.