Girih: the star pattern
Islamic geometric patterns generated by the polygons-in-contact method from a tiling of regular polygons.
The rules it illustrates
Patterns from polygons in contact. To draw a star pattern, cover the surface with a tiling of polygons, draw two lines through the midpoint of every edge at the same angle to it, continue each line until it meets another, and erase the tiling.
The contact angle sets the character. Keep the grid and vary the angle at which the lines cross the edges: a small angle gives broad, blunt stars; a large one gives slender, sharp stars.
Symmetry and the repeat. Choose the symmetry of the principal star (six-, eight-, ten- or twelve-fold) and build the field from a repeat unit that tiles the plane; stars that cannot tile by themselves are completed by secondary shapes in the gaps.
Where it appears in the book
In the styles Early Islamic (Umayyad and Abbasid), Moorish (Western Islamic), Persian Islamic (Seljuk, Timurid and Safavid).
In the chapters The Islamic World.