circles and bundles of radii

Topic:
Circle

starting with radii

The girih method working with a fixed set of polygons creates stars with a fixed number of points. I addition to this system a second method was established. In circle bundles of radii were drawn. Intersection points of these radii define segments, forming polygons. This construction method allows combining stars with a different number of points within one pattern. In the article Girih for Domes: Analysis of Three Iranian Domes the authors Mohammad Hossein Kasraei, Yahya Nourian and Mohamadjavad Mahdavinejad describe this method as the radial girih method or Dast-Gardan girih.
Image
In the example you can see how the pattern  is constructed.
  • Within a unit repeat concentric circles are drawn on every corner point.
  • These circles are divided into congruent sectors.
  • Diagonals in the unit repeat define the center points of additional circles (step A).
  • Connecting intersection points of radii and circles generates a line pattern (step B).
  • This pattern is mirrored on the axes of symmetry if the unit repeat (step C).
The result (step D) is a geometric pattern that combines 12-pointed stars with 9-pointed stars.