Symmetry, in its classical condition, has occurred throughout history as a constructor of order. As an expanded term, it is key to the operational understanding of modern space. Mies van der Rohe's link with this strategy is fundamental and goes beyond his pretended invisibility. An approach to this concept is given through one of his most important works: the German Pavilion for the Universal Exhibition of 1929 in Barcelona, which represented for modernity the culmination of a decade that radically changed the vision of architecture thanks to its inclusive nature. of the paradoxical and the countless connections between art and science. From the latter, he proposes a definition of symmetry as a principle of equivalence between elements. In this definition, the sense of equality collected by Lederman is incorporated as well as that of Weyl's invariance. From this new meaning, an analytical look is projected at the work of Mies and therefore at all modern architecture, opening the door to new geometric realities of the contemporary.
In Mies, not only the paradox of the coexistence of opposites converges, but also the intuition of "building" a space, which he intended to reflect the spirit of the time, and whose genesis is postulated by Noether in her theorem of establishing for each continuous symmetry of the physical laws a conservation law. These continuous symmetries are the (in)visible symmetries of empty space that are apparently revealed as opposition to the order structures of matter, but that participate in the same Miesian aporetic logic of considering it another material, and that are defined as: (i)limited, (in)gravid, (in)finished and (in)material. From this position, factors such as the loss of scale, evident in the latest architecture, as well as its relationship with the virtual, acquire another meaning from symmetry: the paradox of materializing the immaterial; of building the unlimited in "perfectly unfinished" works, whose weightlessness occurs with a marked tectonic emphasis, but is also found in establishing equivalencies between the movable and the immovable, the unreal and the real, or the detail as defining the whole.