Application of the Hidden Layer in the Development of Gireh Based on Iranian Historical Documentation and Monuments

Decorative arts had emerged in various forms in the Islamic world, and Gireh is one of the most complex forms that constitute an essential part of the Islamic arts in the world, which had developed over time. These rely on the geometric rules in the mathematical sciences. One of the most critical issues in the studies of Gireh is the methodology knowledge of their designing and drawing that different researchers emphasize on different methods. Knowledge of the design methodology of Gireh is closely related to its aesthetics and originality. Iranian Islamic architecture significantly contributed to the development of Girehes, but their connection with their methodological knowledge was not obvious. Many scholars consider the method of developing Gireh in Iran based on the radial (Falaki) method, which has remained in the written sources of the last traditional Master of Iran. However, studies on historical documents such as the Topkapi scroll and the Girehs that remained on the Gonbad Soltanieh show that Iranian architects and artists were fully aware of the polygonal method and Gireh production techniques based on it and it used for developing Girehes in Iranian architecture. Therefore, this research seeks to answer the following questions with descriptive-analytical and reasoning methods by collecting information through libraries and field studies: 1- What evidences are left from the past that shows the use of polygonal technique to produce Girehes? 2- How had the application Process of the polygonal technique to the development of Girehes in Iranian architecture? 3- Why did the Iranian Master introduce the radial (Falaki) method to drawing in their books despite the polygonal technique? To answer these questions, after introducing the methodologies of Girehs production, the structure of Gireh is examined from the polygonal technique point of view along with its historical documents. Then, the developing process of Girehs in Iranian architecture is studied based on the development of underlying generative Tessellation. Finally, the radial and polygonal methods are compared, and Their application among the traditional Masters of Iran is examined. Despite numerous studies on the development of Girehs and polygonal technique, the new achievements of this research is new evidence of Girehs left on the surfaces of historic buildings, which presents the application of the polygonal technique in Iranian architecture. These expand the methods of using the polygonal technique to develop Girehs in Iranian architecture. These documents also show a new path in the development of Iranian Girehs, which indicates the use of the Gireh as an underlying tessellation in producing more complex Gireh such as Pili and dual-level Girehes, which is investigated in this study.The Knowledge of Girehes designing and implementation was a family knowledge and available to certain people in the community that architects passed these methods from one generation to the next generation in a secure way to prevent the revealing of this knowledge and usually transfer permission of this knowledge didn’t happen easily. Despite these limitations, methods of designing and applying Girehs were developed in various branches. Although the methods of producing Girehs are extensive and varied, some artists even invented their drawing methods. The four methods are prevalent among designers and researchers of this art and are widely used, including Radial (Falaki), Point-Jointed (Moroccan), the Grid, and the polygonal techniques. The polygonal method is the subject of this research discovered by Ernest Hanbury Hankin when he was visiting an Indian bath and was introduced to the contemporary world. Later, researchers realized that this method is historical by studying historical documents such as the Topkapi scroll. This method is often determined by drawing lines that connect from midpoints to each other’s in the underlying main polygon to create the main stars and the application of pattern lines. The presented method approximately adheres to J. Lee Registration, which creates a given star by identifying the number of sides of the main polygon relative to the number of consecutive sides at the midpoint to the midpoint of the line.Suppose the development Process of Girehs in the Islamic architecture of Iran is examined. In that case, it can be seen that the historical development Process of Girehs began with the formation of patterns on an orthogonal Grid and ended with a very complex tessellation. In addition to observing this method in the Topkapi scroll, the application of this method in the tiling of Gonbad Soltanieh is also evident; the designer kept the underlying generative tessellation in the final design. In addition, the same underlying generative tessellation was used to create another Gireh. Instead of arranging the Alāt (motif) at the midpoint, the Gireh was arranged according to the vertices of the underlying tessellation. It caused three Alāts of Shāmseh to meet at one point. Despite contemporary researchers emphasizing the midpoints of polygons in underlying tessellation in applying the polygonal technique. In addition, the use of Gireh as underlying generative tessellations is also evident in this building to produce Girehs, due to which the next generation of Gireh such as Pili Gireh was created in the Yazd Grand Mosque. In these Girehs, the Alāts of underlying generative Gireh were interweaved by Alāts. Due to this, the number of hidden layers increased. Because in addition to the generative Gireh (underlying tessellation of pili Gireh), there is also another underlying tessellation for the generative Gireh. The last stage of Gireh development is the dual-level Gireh (Shah-Gireh), which uses one Gireh as the preliminary design for the secondary Gireh inside the Alāts of primary Gireh. It is impossible to achieve such a design by using the radial method or applying the symmetry of a fragmented Alāts of Gireh. However, the polygons must be manipulated in the underlying tessellation, which shows the application of the polygonal technique in the history of Gireh development. The polygonal technique is evident from the existence of polygonal tessellation in the Topkapi scroll and Girehs on the remained surfaces of the monument and considering that in the evolution of Gireh in Iranian architecture. The main problem of the radial method is the impossibility to design a new Gireh, the whole process of drawing a Gireh in the radial method is step by step, and the artist needs to follow all the steps, the way of determining the secret line Also is not clear in this method which other arcs are defined. This line in the drawing of the written sources of the masters shows predetermined. In contrast, the polygon method is based on the combination of underlying polygons. Understanding this process makes it possible to place motifs in tessellation, draw the Gireh shape without following a special process, and change the tools based on the underlying tessellation. He came up with various designs. As well ass, it reached various designs by changing motifs based on tessellation. According to the study, the application of the radial method can be for implementing the Gireh on different bases that work be easier based on the tools of architects and artists of the classic era and prevented the disclosure of the design method of Gireh.