Takht-i Sulayman
In 1968 at Takht-i Sulayman, in the north of Iran, an excavation team found a square 13th century 50 cm gypsum plate amid the palace ruins with a geometric pattern incised on it, recognised as a muqarnas design.
In the muqarnas plate found at Takht-i Sulayman: a new interpreatation by Dold-Samplonius and Harmsen
you can read more about the plate and the interpretation of it.
The construction has a diagonal symmetry axis and a large irregular quarter octagon in the upper right corner, so clearly it’s the projection plan of a muqarnas vault.
In the drawing above you can see that the design consists out of squares and rhombi, with isosceles right triangles along the border. But to build a muqarnas you need to split some figures: a square can be split into a large biped and a jug, a rhombus into an almond and a small biped. You can do this in different ways and different autors make different interpretations of the same design. In following applet you can see the interpretation of Silvia Harmsen.
In her dissertation Silvia Harmsen created a computer 3D model out of it. In the applet you can see how vectors lead from the bottom to the apex of the vault.
