6. In determining the criteria for a new architectural beauty, we can rely on the theory of the dialectical synthesis of opposites. The dialectical synthesis is not only a well-known synthesis of the arts. This is a direct form-building synthesis of the opposites of the entire aesthetic range of the architect’s tools presented as tangible and geometric genesis of an architectural composition in the expressive form of reasonable space.

7. Synthesis becomes such a union of two opposite principles, where they not only do not lose themselves, but also acquire new qualities in a new integrity unknown to them before synthesis. The whole is a singularity presented as the synthesis of its parts and properties, which is irreducible to their sum and is manifested in form.

8. Practicing architects can use the principle of synthesis (as the principle of generating new categories from different and opposite phenomena and properties) as another means of searching for new expressive compositions. The dialectical method has the potential to become a key one in the future development of general and applied creativity and composition theories. Architecture is a powerful source of inspiration and creativity in this way.

9. Any category of geometry, starting from a point, is at the same time an abstract mathematical concept, a verbal logical and a visual one. If the visual image of an octagon is some combination of images of a square and a circle, then it is simultaneously beautiful in both respects – both logical and visual. If the dialectical construction shows the movement of categories and beauty in their sense generation, then both visual and material geometry will be a mould, reflection and expression of this movement and this beauty. The geometric concept becomes the point of intersection of logic and aesthetics.