Theoretical Geometry of Special Karbandies in Uncommon Bases (With a Focus on the Mirza Akbar Scrolls)

The main feature of karbandies is the precise geometry and the particular graphic rules in their design and implementation. Different types of karbandies are defined based on their drawing method. Karbandies are used in the regular and unconstrained geometric fields. The pairing method is among the commonly used methods. A close connection between the "design geometry" and "proportions and dimensions of the base of execution" is required to draw the applied geometry in a particular base. Sometimes, the shape of the base is not obtained from the combination of a square and a rectangle. These bases are uncommon and are rarely seen. Under certain conditions and according to the application, the geometry of the karbandi can be implemented on unusual geometric bases and with irregular sides. Several books and papers are published on the geometry of all sorts of karbandies. In almost all of these studies, the usual and regular geometry applied in karbandies has been studied. In this paper, the use of unusual and irregular bases in karbandies has been reviewed. For this purpose, first, the bases of karbandies are categorized, then the data collection about the real instances of irregular bases has been carried out through direct observation and field survey. Also, by using library documents, some samples from Mirza Akbar's scrolls have been drawn. Finally, the geometric system of the samples has been implemented in a 3D modeling software. The magnificent collections of Iranian art at the Victoria and Albert Museum (V&A) include the unique archive of nineteenth-century architectural drawings associated with Mirza Akbar’s scrolls. The drawings in the scrolls present a variety of structural and decorative ideas in Qajar architecture, and also reveal how design methods were used in practice at the time. The purpose of this research is to determine the geometry of karbandies with irregular bases from the perspective of the form of the base plan (theoretical geometry). This unique document of Iranian architecture is the "Mirza Akbar (architect of the Qajar period) Scrolls”. The horizontal and vertical geometry rules of this document are comprehensive, but the application methods of these geometry rules in practice is not determined. There are some examples of unusual and irregular bases of karbandies in these scrolls. The findings of this study indicate that the number of the sides is the most important aspect in distinguishing these applications from the rest of the karbandies. Also, factors such as the number of karbandi’s sides, connection distances, base shape, etc., are important in determining the design method of karbandies. There are three methods to draw karbandi in the bases of irregular polygons: 1) Extending the sides of the work in one direction, 2) Extending the sides of the work in two directions, 3) Connecting the circle splitting points based on the shape of the base and removing some of the bases (the number of bases and the elements of space varies according to the different proportions in the bases. In case of similarity of proportions in the bases, the number of bases varies according to the intended shape for space). While most architects approach the regular architectural solutions on the usual bases to design karbandies before implementation, Mirza Akbar’s drawings follow complex geometry and are implemented in irregular geometry and unusual bases.