## Mauricio Pezo

Diagonal Apology

The word “diagonal” comes from the Greek, (diagonios), a term composed of dia (“through”) and gonal (“angle”). To put it simply, a diagonal is a line connecting two nonconsecutive vertices of a polygon or a polyhedron. Given a rectangular polygon of angles ABCD, its two possible diagonals are AC or BD. Given a rectangular polyhedron of ABCDEFGH, its four possible diagonals are AG, BH, CE or DF. For the geometer it is a straightforward matter to establish that the number of diagonals in a plane may be calculated by subtracting its proximities and reiterations; i.e.: Nd=n (n–3)/2, where n–3 determines that there are no diagonals toward itself nor towards its two adjacent points and where the division by 2 determines that an AB relationship is the same as BA, and therefore does not count. Insofar as it is a geometric prism, a building may be described in at least two dimensions: according to the diagonals of the planes that confine the space or according to the diagonals of the same confined space (equivalent to the volumetric diagonal, something like a “triagonal”).
Published in PRODUCTORA 1. Texts by Mauricio Pezo, Kersten Geers and Miquel Adrià, ARQUINE, Mexico City, 2012