I’ve just come across the Tradigital website (an Arabic publishing studio associated with the Thesauraus Islamicus Foundation and Islamic Art Network) where I have found a very helpful animation of how one Qur’anic illumination pattern is constructed. The design is based on 6-fold geometry from which a 12-pointed star pattern is produced.
Watch the animation here: http://www.tradigital.de/specials.htm
The speed of the animation is quite fast but after watching a few times you could probably give the pattern-making a go yourself using a compass and ruler!
A quick note to say that the Islamic Art Network also has a photo archive of architectural sites in Cairo that may be of interest: http://www.islamic-art.org/PhotoArchive/PhotoArchive.asp