Muqarnas - مقرنس
مقرنس - Muqarnas are a decorative architectural technique developed in Islamic/Arabic cultures and used in ceilings, portals, squinches and minarets. As a complex geometric space-enclosing system مقرنس - muqarnas lend themselves to rectangular (plan view) architectural elements as well as complex polygonal layouts.
مقرنس - Muqarnas are also known as mocárabe. Although some distinguish between the two, the underlying geometric nature is identical. The stylistic differences which they point to are simply feature clusters in a multi-dimensional design space.
The historical and geographic record of مقرنس - muqarnas has been carefully researched and made available on the web by Shiro Takahashi at مقرنس - Muqarnas
My own research and work in مقرنس - muqarnas is due entirely to the thesis of Mamoun Sakkal, "Geometry of Muqarnas in Islamic Architecture". I was in contact with Professor Branko Grunbaum of the University of Washington Department of Mathematics while he was sitting on Mamoun's thesis committee. Branko thought I might enjoy Mamoun's thesis, which turned out to be an understatement. Thank you, Branko, and most expecially thank you, Mamoun, for such fine insights into the geometric nature of مقرنس - muqarnas and for letting me make and keep a copy of your thesis.