Tiling and Tazhib of Some Special Star Polygons: A Mathematics and Art Case Study

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Reza Sarhangi: Tiling and Tazhib of Some Special Star Polygons: A Mathematics and Art Case Study. In: Bridges 2013. Pages 151–158



This article presents the means for covering the interiors of some special star polygons using tiling and tazhib techniques. Several articles study approaches for tiling an unbounded plane using star polygonal motifs. However, the main focus of this article is to present methods for tiling bounded regions, such as the interiors of star polygons, using star polygons themselves to create self-similar designs. In addition, the paper introduces basic techniques of the classical Persian art form, tazhib. An artistic collaboration melding this art form with one of the tilings is included.

Extended Abstract


Used References

[1] Agha Miri, A.H., Designing Tazhib, Yassavoli Publications, 2008, Tehran, Iran.

[2] Bonner, J., Three traditions of self-similarity in fourteenth and fifteenth century Islamic geometric ornament, Proceedings of the ISMA/Bridges: Mathematical Connections in Art, Music, and Science, R. Sarhangi and N. Friedman, eds, Granada, Spain, 2003, pp. 1-12.

[3] Fathauer R. and Nathan S Selikoff, eds, Joint Mathematics Meeting Art Exhibition Catalog 2013, San Diego, California, USA.

[4] Fathauer R. and Nathan S Selikoff, eds, Bridges International Conference Art Exhibition Catalog 2013, Enschede, the Netherlands.

[5] Honarvar, M.R., Symbols of Iranian Illumination and Carpet Designing, Yassavoli Publications, 2011, Tehran, Iran.

[6] Honarvar, M.R., The Illumination Models, Eslimi and Khataei Decorative Designs, Yassavoli Publications, 2008, Tehran, Iran.

[7] Lu, P.J. and P.J. Steinhardt, Decagonal and quasi-crystalline tilings in medieval Islamic architecture, Science 315, 2007, pp. 1106 – 1110.

[8] Maheronnaqsh, M., Design and Execution in Persian Ceramics, Reza Abbasi Museum Press, 1984, Tehran, Iran.

[9] Sarhangi, R., Interlocking Star Polygons in Persian Architecture: The Special Case of the Decagram in Mosaic Designs, Nexus Network Journal, Volume 14, N. 2, 2012, pp. 345-372.


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