### Wall geometry

Walls are the basic structures of spatial creation. The vitruvius trio of durability-expediency-beauty unite in these structures, so they can be examined in many ways: both from the structural, strength and aesthetic side. Although the pattern on the surface of the walls is related to all three of the listed aspects by the contour of the masonry elements, it still seems as if the geometric properties of the patterns have only been examined in special cases. Yet it has been known by architects for more than ten thousand years that this pattern is related to the strength and durability properties of the wall; this is attested by the application of a bond that determines the geometry of brick walls. In my thesis, I attempt to generalize the concept of binding to masonry structures of arbitrary geometry.

The concept introduced in the average space theory of convex mosaics is the ρ cell density, which is the ratio of the cell degree of the mosaic (the average number of peaks of the polygonal masonry element in the case of masonry) to the number of nodes of the mosaic (in the case of masonry, the average number of masonry elements meeting at one point). According to the theory, at least 1 ≤ ρ≤2 for convex masonry elements. Ρ=2 for bonded brickwork and ρ=1 for meshed brickwork.

In my thesis, I determined the value of ρ for masonry with interesting geometry and significance from the point of view of architectural history, and I found that the measured values ranged from 1.68 ≤ ρ≤ 2 bands. Since the value of ρ is determined by the knowledge of the master who made the masonry for any masonry element, I came to the conclusion that the masters sought to maximize the ρ value and, on this basis, the cell density ρ could be considered as a geometric generalization of the binding.

Although it is a well-known fact that the stability of the walls depends to a large extent on geometry, this relationship has not been quantified so far. My investigations can be seen as a step in this direction, as they show that walls with a high value of ρ have proved to be durable.