To quote Wikipedia (as of 1 Jan 2025):

Girih tiles are a set of five tiles that were used in the creation of Islamic geometric patterns using strapwork (girih) for decoration of buildings in Islamic architecture.

Many sources suggest that the set of Girih tiles has precisely five members (the core). However, Lars Eriksson disagrees, having prepared an important report, a combination of original work and literature review, which points out that these are not sufficient to describe a number of extant examples of Girih tile use. Eriksson goes on to summarize additions proposed by some other researchers, and to offer some of his own.

Meanhil, the present author has an older, separate paper on a related topic, convex deciphis.

The present report is a gallery of selected Girih tile shapes and variations of strapwork, not all of them original, observing parameters characteristic of Girih tiles:

• For tiles:
  • Each tile is a simple polygon.
  • All edges are of equal length.
  • The angle between any two edges is a multiple of 36 degrees.
• For straps:
  • Every edge is met by two straps.
  • The angle between a strap and an edge it meets is 54 degrees.
  • All straps are straight, never curved. However, a strap might have one sharp bend.
  • A strap connects one edge of a tile to another edge.
  • One strap may cross another, but there are no intersections with an odd number of straps.

As a consequence, when one strap crosses another, or when a strap has a bend, the angle must be a multiple of 36 degrees.

Each tile shown in the table below has a designator, which has three parts:

• a number denoting how many edges the tile has;
• a letter denoting the tile's shape;
• a number denoting the strap pattern; if the number is zero, the straps are omitted.

For each shape of tile an area a is given, assuming that each edge is of length one. Two useful symbols are p = ¹⁄₂ sin (72°) and q = ¹⁄₂ sin (36°).

The core tiles have an asterisk appended to their designators.

As for the aesthetic merits of each design, opinions will vary.

4A a = 2p + 0q
4B a = 0p + 2q

5A a = 3p + 1q
5B a = 1p + 1q

6A a = 4p − 2q
6B a = 2p + 4q
6C a = 4p + 2q

7A a = 1p + 3q

8A a = 6p + 6q
8B a = 6p + 2q		compare
8C a = 2p + 6q
8D a = 6p − 2q
8E a = 2p + 2q

10A a = 10p + 10q
10B a = 10p + 6q
10C a = 10p + 2q
10D a = 10p + 0q
10E a = 4p + 8q		compare
10F a = 2p + 4q