Bridges 2011 Short Paper

Lu and Steinhardt introduced the term ``girih tiles'' to describe the set of equilateral polygons that structures a colorful two-dimensional decagonal tiling on the Darb-e Imam in Isfahan, Iran (1453 CE) with distant roots in the five-fold symmetries articulated in brick on the Gonbad-e Qabud, a tomb tower dated to the late 12th century CE located at Maragha in western Iran. Their work seeks to establish the early existence of quasi-crystalline tilings long before such means of covering the plane were understood mathematically in the West. Questions remained unanswered as to whether those who constructed these monuments were aware of the mathematical significance of their constructions. Lu and Steinhardt, as well as Makovicky and Bonner, who legitimately claim prior discovery of these decagonal tilings and their sub-grids, all missed the fact that the tower is itself decagonal. This brief paper draws attention to the relationships among architectural form, geometric ornamentation, and Qur'anic inscriptions in assessing the cultural significance of the Gonbad-e Qabud.