1. From Geometry to Architecture and Construction

2. Consider a vertical section of polyhedrons that correspond to columns having different shift states. Each polyhedron is divided in four equal height zones.

3. The bottom zone, which will be referred to as the "floor zone", includes a space-truss that follows the 3D construction grid, while it accommodates the electromechanical infrastructure of a building construction. The remaining three zones represent livable space. Now we are going to compare the section of an arbitrary polyhedron, of which the livable space is marked in blue, with the section of the same polyhedron in the case in which both left hand and right hand polyhedrons correspond to columns having the same shift states. Vertical boundaries, in the latter case, are represented by the red line. In the different-shift-state case the polyhedrons region is increased by the triangle marked in red, while decreased by the triangles marked in black. Note that the red triangle roughly corresponds to the human height, while the black triangles are either out or at the limit of human range.

4. Furthermore, the maximum length is gained at the work level which is the most critical for human activities. A similar gain occurs for all polyhedrons, which results in significant gain of architectural space.

5. Ergonomic use of architectural space of this kind is illustrated here.

6. Now we are going to examine some aspects of the relation of the built space with environmental factors. In this picture, right hand polyhedrons represent non built space.

7. Consider the case where both left hand and right hand polyhedrons have the same shift states. This results in vertical boundaries of the built space. Suppose that the two upper zones of the built polyhedron correspond to a window … … allowing penetration of solar light / energy into the built space.

8. In the case of the different-shift-state case the boundaries of the built space are oblique.

9. Potential penetration of solar light / energy into the built space is increased, even if the window's area remains the same, as the window is now oriented to the sun. This implicitly increases the variability of the design, as more design cases (system's states) become light / energy effective.

10. Now let us return to the same-shift-state case …… to represent penetration of solar light / energy into the open space.

11. Comparing this case with the different-shift-state case, where the upper floor zone has been properly adjusted according to the construction grid, … … we can see that the amount of solar light / energy available to the open space can increase. This has also implicit beneficial effects on the variability of the design. Due to the aforementioned benefits of the different-shift-state case, we can adopt the principle that this case always characterizes the relation between open and built space. The particular principle, viewed as a constraint, seems to decrease the system's variability. However, the same-shift-state case can be restored through the proper use of the construction grid.

12. The possibility to adjust a floor zone according to the construction grid allows extension of the floor zone in the open space, which results in horizontal transition between open and built space …

13. … practically restoring the same-shift-state case. In fact, the possibilities of the fine-grained construction grid, not only in extending a floor zone …

16. … but also in relaxing the vertical dependence between polyhedrons, by allowing horizontal shift of boundaries, vastly increases the system's variability.

20. Continued in Section_4_EN.PPS