Systematic architecture is based on the cube (with its distortions), the sides of which intersect orthogonally, with horizontal utility areas (floors) and vertical intersections of space (partitions).

A spatial structure attempts to integrate the diagonals (oblique forms) frequently occurring in practice within a particular system, such as stairs, ramps, inclined roofs, oblique utility areas, constructive diagonals in grids.

If the empty spaces of lattices are to be used, this results in a conflict between constructive diagonals and space to be used, between statics and use. Spatial diagonals are excluded, flat diagonals are located in the vertical surfaces (walls) of an habitable structure with horizontal planes and vertical separations.

A geometrical figure with orthogonal faces is the prism, for the positions

• a- quadratic or octagonal prism
• b- triangular- or hexagonal prism
• g- rectangular prism
• d- pentagonal or decagonal prism

An architecture developed on a spatial grid according to my definition can be varied:

• through the choice of positions (a, b and g) and others
• through specific distortion
• through the size of the elements to adapt to the static stress
• through the type of the parts (1D bar or rod, 2D surface, 3D bodies)
• through the selection between crystalline (Ö1, Ö2, Ö3) and quasicrystalline lattices (1/j, 1, j, j²)
• through progressive/ degressive serial arrangement
• through transition to "deconstructivism"
• through the combination of compression and tension members of different constructional elements.

Even a "deconstructive" or amorphous structure is only usable if it has horizontal utility areas..

USABILITY
LIBESKIND