girih tiles

Five tiles

  • a regular decagon with ten interior angles of 144°;
  • an elongated (irregular convex) hexagon with interior angles of 72°, 144°, 144°, 72°, 144°, 144°;
  • a bow tie (non-convex hexagon) with interior angles of 72°, 72°, 216°, 72°, 72°, 216°;
  • a rhombus with interior angles of 72°, 108°, 72°, 108°; and
  • a regular pentagon with five interior angles of 108°.

These modules have their own specific Persian names: The quadrilateral tile is called Torange, the pentagonal tile is called Pange, the concave octagonal tile is called Shesh Band, the bow tie tile is called Sormeh Dan, and the decagram tile is called Tabl.[1] All sides of these figures have the same length, and all their angles are multiples of 36° (π/5 radians). All of them except the pentagon have bilateral (reflection) symmetry through two perpendicular lines. Some have additional symmetries. Specifically, the decagon has tenfold rotational symmetry (rotation by 36°); and the pentagon has fivefold rotational symmetry (rotation by 72°).