Escher depicted lizards, different in color, but not distinguishable in shape, placed on a plane according to symmetry transformations.

Thus, the symmetrical ones include such regularities, the basis for the construction of which is based on a certain type of symmetric transformations. Symmetrical transformations on the plane and in the space of rotation around the axis, transfers, mirror reflections, grids and spirals serve as the starting points for the most important techniques of composition, for example, methods of proportionation, rhythmic articulations, the method of geometric similarity, etc.

In fact, any group of elements satisfying the same construction rule can be called symmetric. However, if we adhere to the restrictions accepted in science, we should add: despite the fact that all the elements are of the same color.

The concept as a whole can have meanings characterizing the degree of orderliness (as a quantitative and qualitative assessment) of a composition, any architectural form in terms of harmony, balance, proportionality, unity. In the system of concepts of architectural composition, symmetry plays a basic role precisely because of the richness of its meanings, which include new aspects along with traditional ones.

So gradually we comprehend architectural symmetry as the semantic integrity of the fundamental concepts of the profession.

Traditionally, symmetry in architecture is understood only as a kind of geometric regularity. With the involvement of one of the main meanings of the general scientific concept of symmetry: the idea of symmetry as a form of any pattern of structural, semantic, abstract, etc. – the concept of architectural symmetry acquires new meanings and can, along with the traditional idea of the symmetry of the object of contemplation or creativity, include the idea of symmetry as a feature of thinking, as properties of a person perceiving or creating a symmetrical the form.

Let’s try to outline the idea of symmetry in architecture as a kind of unified conceptual structure. We are talking about a concept that encompasses the totality of many meanings, meanings, relations of a special scheme of knowledge within the boundaries of the existence of the concept itself in the profession.

Professional understanding of the concept of symmetry consists, in our opinion, in a kind of interpretation of special terms and meanings in the categories of architecture. The difficulty, however, lies precisely in the universality (by definition) of symmetry: the applicability of its ideas to the interpretation of all kinds of laws, any order of concrete facts, abstract ideas, plot analogies, etc. Observation of the laws of symmetry in professional thinking, creative traditions expands the traditionally established understanding of symmetry due to its non-geometric interpretations.

In the following presentation, three aspects will be considered – three forms of “existence” of symmetry in architecture. We called the first aspect “geometric”. Here symmetry appears as an objective structural regularity inherent in the structure. The second aspect is “socio-cultural”. This non-geometric essence of symmetry encompasses subjective and objective patterns in professional creativity as invariant cultural meanings that formalize the principles of compositional thinking. The third aspect is “instrumental” – it represents symmetry as a widely understood process, a way of ordering: techniques of project graphics, thought schemes, systematic consideration of a project task, etc.

To clarify the unity of these aspects, it seems appropriate to use an analogy of architectural symmetry with language as a system of signs, a way of exercising professional consciousness. At the same time, the visual elements of geometric symmetry are correlated with the dictionary as a “palette” of graphic and constructive possibilities of symmetry. In the “geometric” aspect of our concept system, it is assumed to describe this dictionary, the pictorial function of symmetry in the structure of architectural form. The meaning and meaning of visual images of symmetry is in charge of a different, non-geometric essence of symmetry, which reveals the relationship of the image to the depicted, i.e. the correspondence of visible patterns to mental structures. This symbolic function of symmetry reveals the semantics, socio-cultural content of the usual construction techniques and professional “mental habits” of compositional thinking.

The symbolic function of symmetry is considered in the “socio-cultural” aspect. And, finally, symmetry is a process as a means of realizing professional consciousness – an instrument of compositional thinking correlates with speech and as a means of graphic design of architectural thought with syntax. The “speech”, conversational function of symmetry is considered in the “instrumental” aspect. These diverse layers of our ideas about symmetry have a single geometric basis in an architectural work.

Conditionally allocated positions, of course, do not exhaust the entire semantic diversity of architectural symmetry, but for a start they can serve as nodes of the general structure of the concept as a mental scheme. Our goal is to build a certain system, a canvas for generalizing disparate ideas.