The Geometry of Karbandi in Persian Architecture; Response to the Challenges of Conventional and Stellar Karbandi

Karbandi is one of the original and ancient arched elements in Persian architecture which is formed based on a network with harmonic geometry and in addition to architectural function, it also has structural behavior. However, there are ambiguities about the geometry of this architectural element that should be addressed with targeted research. One of these ambiguities is to determine how the geometry of different types of Karbandi is mapped; according to the available information, different types of Karbandi cannot be easily distinguished. The conventional and Stellar Karbandi are of the controversial issues in recognizing the geometry of Karbandi in Persian architecture. The present study aimed to identify and discover the geometric relationships in the conventional and Stellar Karbandi based on actual examples as well as study and analyze the geometric characteristics of different types of them. The necessity of the present study is to clarify how the geometry of different types of Karbandi is mapped to provide a comprehensive classification for it based on executed examples. The results of the present study showed that the difference between the two types of conventional and Stellar Karbandi is the connection distance between the points of division on the circle. It's easy to recognize this note in rectangular and squares bases; if the length of the rectangle or one of the sides of the square is in front of segments of the circle and the relation of equality is established between the number of segments of a circle in front of the length of the rectangle and the connection distance between the division points of the circle, the simple conventional Karbandi will be obtained. But, in non-rectangular base, firstly, the base must be divided into two or more identical intersecting rectangles, in this case, a length of one of these rectangles is considered as a criterion to recognize the type of Karbandi. If the relation of equality is established between the number of segments and the connection distance, extension conventional Karbandi will be obtained. If the relation of equality is not established, the obtained Karbandi is Stellar Karbandi. In this case, there are mathematically different scenarios that were examined. By examining the aforementioned cases, it has been proven that Tarkin vault is also of Stellar Karbandi. Therefore, another category called "Tarkin" was added to the other two categories of Stellar Karbandi, namely, "Discrete" and "Continuous".