The Geometry of Cuboctahedra in Medieval Art in Anatolia

Abstract

Numerous examples of cuboctahedra found in medieval-era buildings whose dates range from the early twelfth to the early fifteenth century across in Turkey indicate the significant use of such geometrical entities. Here we focus particularly on cuboctahedra with carved-out surfaces. The results show that although the unit cell, which is a combination of cubes and tetrahedra, sufficiently explains all examples, the octahemioctahedron and stella octangula strengthen the possibility of tetrahedral packing with its dual network and indicate a "vector matrix", as suggested by R. Buckminster Fuller. Therefore, their prevalent use as a "geometric solid" in a hollow cube frame and their appearance as an envelope of either tetrahedral packing or highly complex surfaces reveal almost 800-hundred-year-old examples of cuboctahedra as a Vector Equilibrium (VE) producing Isotropic Vector Matrix (IVM).