What would be more interesting for our presentation's purpose? To analyze how math has been used in the past or to attempt new applications for the present? This is the question being put forward here. I believe that form in architecture can be explored directly in three dimensions if one can manage an accurate and versatile perspective method.
2D drawings and 3D models have been used either to represent or build architecture since ancient times. These are usually made at any scale, whereas perspective cannot be scaled, it allows the truthful render of a form in proportions. Perspective mainly allows the designer to visualize a building within an imaginary space.
Architects frequently use perspective when the design process almost comes to an end, to get an idea of how a building could be seen in reality. However the customary use of 2D projections along the design process compels designers to visualize forms fragmentarily. On the contrary, the architectonic example we are about to present here was not based in 2D projections nor a preconceived form, it was rather the result of exploring form directly in perspective, of using mathematics to visualize form beyond 2D. The Città Ideale perspectives, attributed to Piero della Francesca, are one of the finest examples we have of architectural forms created in perspective.

Figure: Fractalizing the hypercube (drawing by Tomás García-Salgado)