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For centuries, transforming the cubic space to a spherical dome was a matter of challenge, structurally and formally. The squinch was the primary solution to build the ‘divine’ sphere over basic cubic chambers in palaces and mosques in Iran (Memarian et al. in J Iran Archit Urban 8(2):75–84, 2017) that mediated its geometric transformation. In this research, the authors will answer the question of where and how did this innovative transformative squinch, or as it will be defined here, ‘
chapireh
,’ become quintessential for all generative Islamic tectonics like
karbandi
and ornaments like
muqarnas
. For that purpose, we simulated and modeled different types of Islamic tectonics and their bottom-up formation process from early generations of the transformative chapireh to the complex evolved version of the tectonic. Towards this end, we approach chapireh through a shape grammar as a generative computational tool for forming new tectonics out of basic Islamic modules and simple rules.