A New Approach to Drawing 10 Point Girih Motifs Using Baseline ‎Method

Decorations in Islamic‏ ‏art are often built on combinations of repeated squares and ‎circles, which may be overlapped and interlaced to form intricate and complex patterns. ‎Based on the shapes drawn from the circle, the earliest geometrical forms in Islamic art were ‎occasional isolated geometric shapes such as 8-pointed stars and lozenges containing squares. ‎These date from 836 in the Great Mosque of Kairouan, Tunisia, and since then have spread all ‎across the Islamic world. In 1086, 7 and 10 point girih patterns (with heptagons, 5 and 6 ‎pointed stars, triangles and irregular hexagons) appear in the Jameh Mosque of Isfahan. 10 ‎point girih became widespread in the Islamic world and this kind of girih (10 point girih) is ‎the subject of this paper.‎
Girih are elaborate interlacing patterns formed of five standardized shapes. The style ‎is used in Persian Islamic architecture and also in decorative woodwork. Girih designs are ‎traditionally made in different media including cut brickwork, stucco, and ‎mosaic faience tilework. In architecture, girih forms decorative interlaced strap work surfaces ‎from the 15th century to the 20th century. Most designs are based on a partially hidden ‎geometric grid which provides a regular array of points; this is made into a pattern using 2-, 3-‎‎, 4-, and 6 fold rotational symmetries which can fill the plane. The visible pattern ‎superimposed on the grid is also geometric, with 10 and 12 pointed stars and a variety of ‎convex polygons, joined by straps which typically seem to weave over and under each other.‎
A recurring motif is the 8-pointed star, often seen in Islamic tilework; it is made of ‎two squares, one rotated 45 degrees with respect to the other. The fourth basic shape is ‎the polygon, including pentagons and octagons. All of these can be combined and reworked ‎to form complicated patterns with a variety of symmetries including reflections and rotations. ‎Such patterns can be seen as mathematical tessellations, which can extend indefinitely and ‎thus suggest infinity.‎
As it cited above, in this article, the method of 10 point girih drawing is essayed and ‎in order to maintain and ease the use of this lasting legacy in contemporary Iranian Islamic ‎architecture, the question arises as to how to minimize the tools and stages of 10 point girih ‎drawing, invented a method for drawing schematics in addition to speeding up the practice of ‎drawing and applying motifs.‎‏ ‏Authors, in response to this question, have developed a method ‎called the baseline method (eighteen – eighteen Method), which presented an original pattern ‎for drawing 10 point girih motifs. The most difference between this new method and ‎traditional method is that in this method, girih would been drawn without using circle and ‎compasses which results in a higher speed for girih drawing.‎
In this research, a combinative method has been used; the data collection is based on ‎library documentation studies, and a kind of logical methodology based on mathematical ‎relationships and mathematical proportions, is used for presenting a suitable model for ‎drawing 10 point girih.‎