Islamic Geometry: Girih Tiles
The Persian word for knot is Girih. It involves combinations of 5 differently shaped tiles, one of which being the rhombus, particularly used to make complex mosaics. One of the earliest examples being the 1453 Iran in the shrine of Dark-e Imam.
Pictured above is a pattern replicated from the shrine. Notice that it's aperiodic, meaning that it doesn't repeat or maintain translational symmetry (only rotational).
There are similarities in medieval Islamic architecture and comparatively modern mathematical design, believe it or not. Similarly aperiodic, there are Penrose Tilings and 3D Wieringa roofs. They show that an “orthogonal projection on the horizontal plane for the thick and thin rhombus" have be used in Islamic mosaics since long before (Moradzadeh & Ebrahimi, 2020a). We will explore these similar patterns more in the Applications.
