The issue of space partitioning underlies the architectural planning and design of buildings, structures and spaces intended for human activity. This thesis explores the phenomenon of periodic dual spaces, the periodic three-dimensional networks that represent their inner structure and the partition between them. It is assumed that every dual-pair of networks, (often referred to as complementary or reciprocal pairs), (Figure 1) can be separated and partitioned by a continuous smooth hyperbolic surface. The thesis is focused on the unique phenomenon of identical dual spaces and the related network pairs, and the hyperbolic surface-partitions separating them, and thus dividing the entire space into two identical (complementary) sub-spaces (Figure 2). The adopted approach implies investigation of order and organization of these spaces and related parameters, their inner and overall symmetry structure and the nature of the 2-manifold partitions, dividing between them. An additional central goal was to conduct a systematic exhaustive search of possible (thus defined) surface-partitions, in order to establish their range of existence and to facilitate their classification. The study described in this thesis comprises three stages.