The issue of partitioning space underlies the architectural planning and design of structures and spaces allocated for human activity.
This thesis focuses on the phenomenon of periodic dual spaces and the partition between them. Periodic three-dimensional networks can represent the inner structure of these spaces. Each periodic network in space has only one dual network (dual networks are discussed in the thesis). These network pairs are often referred to as complementary or reciprocal networks. Every dual network pair can be partitioned and separated by a smooth hyperbolic surface.
The thesis explores the unique phenomenon of identical dual networks and the hyperbolic surface separating them and dividing the space into two identical subspaces.