# Pablo Lorenzo-Eiroa

Multidimensional Space

Spatial organization plays an essential role at a cognitive level,
presenting limits to how architects and other disciplines measure and
reference dimensions in space. House IIB is an experimental project
that integrates two topological mathematical surfaces. Each of the
three Cartesian planes (XY, ZY, ZX) propose an initial organization
with a central void. Each of the centers and corners of the planes
become continuous with each other following a Boy Topology. A Boy
Surface can be mathematically scripted through various degrees of
curvature. This experimental house integrates two forms of scripting
the surface, as straight lines and as curves, discovering that they
can become continuous with each other.

Multidimensional Space: -X, X -Y, Y -Z, Z

House II version B is an architecture experimental house project
that integrates within a single mathematical surface a
twelve-fold-surface topology, interconnecting two mathematical Boy
Surfaces. A first mathematical surface integrates three Klein
topologies and six MÃ¶bius topologies into a continuous sequence.
The surface is scripted to reference but also displace the three
Cartesian coordinate planes XY-YZ-XZ. The first mathematical
surface is developed through double curvature, the second
mathematical surface contains the first one and is developed as a
series of three Cartesian continuous volumes where interior and
exterior, center and periphery are continuous with each other.