# Kalon mosque - niche in the east iwan - gp

Topic:
Geometry
Now let's draw the attention to a niche in the east iwan of the Kalon mosque. On the picture right you can see that the ground plan of the niche is octagonal with standing sides. Above the niche is curved and the sides coincide in the apex. Drawing a geometrical pattern requires exceptional solutions.
In the lower part, with square sides, the pattern is constructed with regular dodecagons (blue), regular octagons (green) and ties (violet). In the upper curved part the sides of the niche become smaller. One can deal with this by gradually using different polygons in the pattern.
• In a first layer the octagons (green) are replaced by heptagons (orange).
• In a second layer only dodecagons are used (red), filled by ties.
• The third layer uses heptagons (orange).
• The forth layer uses only pentagons (yellow).
• The niche is crowned by a half octagon.
Within the polygons of every layer corresponding stars are constructed. So in the niche you can find as well 5-pointed, 6-pointed, 7-pointed, 8-pointed as 12-pointed stars while the patters looks very regular and balanced. The technique to combine different stars in curved surfaces is also used in domes (see the chapter domes﻿ in my GGbook on geometrical patters).