Now let's draw the attention to a niche in the east iwan of the [url=https://orientalarchitecture.com/sid/1323/uzbekistan/bukhara/kalyan-mosque]Kalon mosque[/url].[br]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.[br]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).[br]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.[br][list][*]In a first layer the octagons (green) are replaced by heptagons (orange).[/*][*]In a second layer only dodecagons are used (red), filled by ties.[br][/*][*]The third layer uses heptagons (orange).[/*][*]The forth layer uses only pentagons (yellow).[br][/*][*]The niche is crowned by a half octagon.[/*][/list]Within the polygons of every layer corresponding stars are constructed.[br]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. [br]The technique to combine different stars in curved surfaces is also used in domes [br](see the chapter [url=https://www.geogebra.org/m/kxp4qekc#chapter/446619]domes[/url] in my GGbook on geometrical patters).