Nexus Network Journal

, Volume 20, Issue 1, pp 125–152 | Cite as

The Geometry of Cuboctahedra in Medieval Art in Anatolia

  • Hakan Hisarligil
  • Beyhan Bolak Hisarligil


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).


Geometry Architectural ornament Archimedean solids (cuboctahedron Rhombic dodecahedron) Polyhedron/polyhedral Medieval art Anatolia 



We thank Kim Williams and the reviewers for their thorough and constructive comments, which give us fresh ideas and more unexpected results in this challenging paper. All photographs and images are by the authors except Fig. 1a published with the reprint permission kindly granted by Suna and İnan Kıraç Foundation Anatolian Weights and Measures Collection.


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Copyright information

© Kim Williams Books, Turin 2017

Authors and Affiliations

  1. 1.Atilim University Department of Architecture Kizilcasar Mah. IncekAnkaraTurkey

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