Çifte Minareli Medrese, Sivas/Turkey

Setting up the rectangular grid, showing where the ratio Sx/Sy = 1/sqrt(3) comes from

If you want the dodecagons meet in their sides mid-points as in the original pattern , the proportions are as follows, where

*r*is the radius of dodecagonal circumcircle and*2a*is the size of one side. From the equation for the size of the inradius of a polygon;inradius =

**r*cos(π/n)**Hence,

**sqrt(r²-a²) = r*cos(π/12)**

**a = sqrt(r-(r*cos15))**

We found the relationship between the side length and the radius of a dodecagon

We now need to define a grid in form of

*r*and*a*. We know if we want the dodecagons to meet up in their sides midpoints distance between their centers would be**r+a*sqrt(2)**Which is,

**r+(sqrt(r-(r*cos15))*sqrt(2))**

This equals to the horizontal spacing of the grid (2x in the first picture).

ghx file

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