Darb-I Imam Shrine

• Finite Local Complexity (FLC)
• Finite Rotations
• Girih
• Polytopal Tiles
• Self-Similar Substitution

Info

The substitution tiling was derived from a mosaic at the Darb-i Imam Shrine in Isfahan, Iran. While the shrine dates back from 1453, [Lau2018] argues that the mosaic was created much later between 1715 - 1717.

The tiling relies on the regular decagon and two hexagons and has individual dihedral symmetry ‘$D_{10}$‘. It was published in [LS2007] but the complete set of substitution rules can be found in [Ten2008] .

Substitution Rule

Patch

download vectorformat Darb-I Imam Shrine

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References

[Lau2018]
Lauwers, L.
Darb-e Imam Tessellations: A Mistake of 250 Years
Nexus Network Journal 2018, 20, 321–329, https://doi.org/10.1007/s00004-018-0391-y

[LS2007]
Lu, P.J.; Steinhardt, P.J.
Decagonal and Quasi-Crystalline Tilings in Medieval Islamic Architecture
Science 2007, 315, 1106–1110, https://doi.org/10.1126/science.1135491

[Ten2008]
Tennant, R.
Medieval Islamic Architecture, Quasicrystals, and Penrose and Girih Tiles: Questions from the Classroom
Bridges Leeuwarden: Mathematics, Music, Art, Architecture, Culture 2008, 297-304, http://archive.bridgesmathart.org/2008/bridges2008-297.html

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