Cross Pattern 4

Minbar of Mihrimah Sultan Mosque, Istanbul, Turkey

5&10 Point Stars

Minbar, Alâeddin Mosque,  Konya, Turkey

Sırçalı Medrese

Photos from Sırçalı Medrese, Konya, Turkey

Karatay Medrese

Photos from Karatay Medrese, Konya, Turkey

Interlocking Arrows 2

Gök Medrese, Tokat, Turkey

Cross Pattern 2

Tomb of Halifet Gazi, Amasya, Turkey

Interlocking Dodecagons

Çifte Minareli Medrese, Sivas/Turkey

interlocking dodecagons from caglar on Vimeo.

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

interlocking dodecagons.ghx

Interlocking Octagons

interlocking octagons from caglar on Vimeo.

 

The spandrel of Muradiye Camii (Muradiye Mosque) in Bursa/Turkey.

Stone carving on the portal niche of Darüşşifa (hospital) in Divriği/Turkey.(Slightly different from the pattern in the animation)

  The pattern is based on four point stars in contact.

 

ghx file
interlocking octagons.ghx

sixfold pattern on hex-grid

sixfold pattern on hex-grid from caglar on Vimeo.


A common hexagon based pattern found in beautiful tilings of Yeşil Cami (Green Mosque) in Bursa/Turkey. Equilateral triangles are arrayed around a regular hexagon.

 

ghx file

sixfoldpattern.ghx