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, 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
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
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.