Hagia Sophia and the Khatam

Islamic patterns or geometry is one of the three distinct disciplines of Islamic art the others being calligraphy and Islimi.

The eight pointed star or Khatam is used widely in Islamic architecture.  In simple terms it's construction comprises two congruent squares, interposed, one of which is rotated through 45deg.  The khatam can be progressively broken down in order to find the classical elements  of 8-fold symmetry.  Several patterns can emerge through the extensions of the parallels thereby forming a network of lines, at the intersection of which several shapes or designs emerge.