Girih is one of many Islamic Geometric Patterns used to decorate many mosques. Its basic form is a set of five tiles that can tessellate, or cover a surface completely without gaps or overlaps. These polygons are: pentagon, decagon, an irregular hexagon that some call a spindle, a rhombus, and a bowtie. What sets Girih aside from other tiles is that it incorporated strapping that forms a weaving knotted structure similar to Celtic knots.

Girih tiles are based on the angles of a regular pentagon (i.e., muliples of 2pi/5 or 72°). All edges of the tiles use these angles. The strapping uses a set of angles exactly halfway between the edges angles, so again all strapping for the knots is set at only five angles (i.e., odd multiple of 2pi/10 or 36°).

There is some debate on the number of polygons included within the Girih set. The five shapes has been proposed by Peter J. Lu and Paul J. Steinhardt in their study of Islamic patterns as they apply to quasichrystalline structures. The creation tool included a sixth polygon, the lozenge or thin rhombus, which is useful for some designs.

WikiPedia has an example of how to construct a Girih pattern using a compass and straight edge. This pattern has been found on some middle eastern tombs. It is interesting, because when you break down the pattern by bisecting the crossover points, the pattern breaks down to a set of equilateral triangles. This is not compatible with the Lu/Steinhardt polygon tiles, because here the angles are 60° apart.

Simple Example of Girih Construction from WikiPedia

Using the Turtle Graphics IDE one can create a triangular tile with the primary strapping in dark blue and a secondary strapping pattern in red. The boundaries of each equilateral triangle are shown in light blue and the pattern on every triangle is the same.

Triangular Girih with two levels of strapping design

Girih Tool (under development)

This tool may be used to create Girh tile designs.

Catalog of Girih Designs

This catalog is series of Girih designs to investigate what is possible in terms of basic symmetry (translational, mirror, rotational). Much of this catalog is devoted to patterns with rotation symmetry.

More Information

More information about Girih and Islamic Geometric Patterns can be found on Wikipedia and other Internet sites like PatternInIslamicArt.com.

Girih

cutting speeds 1/8” plexiglass 350/25% for etching (too deep for me) 20/80% cutting

Girih

Girih Creation Tool

The Girih Creation Tool is used to create designs using Girih tiles. It is inspired by the girih tiles invented in the 10th century or so. These tiles have been used in the architecture of many structures in the Middle East especially mosques and tombs. This tool is a work in progress and has some rough edges. A commercial tool is available for Macintosh computers which is more polished and has some interesting features.

Girih

Girih SVG file

Grih likes SVG format. It allows the designs to be easily scaled without losing resolution. This is important as designs are applied to different sizes of print media whether the printing is done with a ink jet printer, laser printer, laser cutter, knife cutter, 3-D printer, etc. SVG offer another advantage for interactive media. They can be animated fairly easily on some browsers. Some experimentation is needed here to determine what can be done with each browser type.