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GeoGebraGeoGebra Klaslokaal

Sultan Han - from 2D to 3D

from tiling to muqarnas

In the nexr drawing you can se how the scheme of the muqarnas in Sultan Han is built up as a creative tiling of rhombuses around an 8-pointed star. The connection with the rectangular border is realised with just two extra shapes: a triangle and a kite.
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On the drawing of Shiro Takahashi you can see how this tiling is turned into muqarnas. The lines that mark the tiers don't just run straight through the drawing.
  • All squares are intersected in such a way that in 2D they are devided into a large biped and a jug. This makes they are realised in the muqarnas in two different levels (see biped and jug)
  • The rhombuses are treated in two different ways. - The lying ones match with the basic shape of the rhombus. - The standing rhombuses are intersected by the lines of the tiers. In the muqarnas they are realised in two different levels (see biped and almond)
In the next applet you can see the lines of the tiers as well as how squares and rhobuses are realised. Note that in the 2D drawing vertical lines ans sides of the muqarnas aren't shown, as neither the sides nor the standing edges of a cube are shown in top view. The vertical sides of the jugs that support the rhombuses become lines between a square and a lying rhomus in the drawing.