Another look at Pentagonal Persian Patterns

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Jean-Marc Castera: Another look at Pentagonal Persian Patterns. In: Bridges 2016, Pages 325–330.



This approach of Pentagonal Persian Patterns is an alternative to the famous PIC theory. However, it turns out that the classification of pattern families and sets of tiles used is close to the one used by (at least some) masters of the art in Iran. A very simple transformation of one of these sets produce a new style of patterns. Then we dissect each tile of a specific set into rhombi, respecting the rules of the Binary tiling (not the Penrose tilling). Thus, applying the concept of X-Tiles to these rhombi, we get an equivalence relation between two families of traditional patterns.

Extended Abstract


 author      = {Jean-Marc Castera},
 title       = {Another look at Pentagonal Persian Patterns},
 pages       = {325--330},
 booktitle   = {Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture},
 year        = {2016},
 editor      = {Eve Torrence, Bruce Torrence, Carlo S\'equin, Douglas McKenna, Krist\'of Fenyvesi and Reza Sarhangi},
 isbn        = {978-1-938664-19-9},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 url         = { },
 note        = {Available online at \url{}}

Used References

[1] J. Bonner, “Three traditions of self-similarity in fourteenth and fifteenth century Islamic geometric ornament”, Proc. ISAMA/Bridges, (Granada, 2003), eds. R. Sarhangi and N. Friedman, pp. 1–12, 2003.

[2] J. Bonner, “The Historical Use of Polygonal Sysem to Create Islamic Geometric Patterns”, Les tracés de l’Arabesque géométrique, pp. 73-83, Académie des Arts Traditionnels, Casablanca, 2013.

[3] J.-M. Castera, “Flying Patterns”, Proc. ISAMA/Bridges, Coimbra, 2011. Can be downloaded from

[4] J.-M. Castera, “Persian Variations”, Nexus Network Journal pp 1-52, 2016

[5] P. R. Cromwell, “Cognitive Bias and Claims of Quasiperiodicity in Traditional Islamic Patterns”, The Mathematical Intelligencer, December 2015, Volume 37, Issue 4, pp 30-44.

[6] E. H. Hankin, “The Drawing of Geometric Patterns in Saracenic Art”, Memories of theArchaeological Society of India, Vol 15, Government of India, 1925.

[7] C. S. Kaplan, Computer Graphics and Geometric Ornamental Design, PhD thesis, 2002. Can be downloaded on

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

[9] H. Mofid, M. Raieszadeh, Revival of the Forgotten Arts: Principles of the Traditional Architecture in Iran According to Hossein Lorzadeh, Mola Publications, Tehran, Iran, 1995 (In Persian).


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