Geometric design of a masonry lattice space dome titled KARBANDI in Persian architecture

Abstract

Studies of historical buildings in Persian architecture have resulted in knowing a kind of masonry structure with a harmonic lattice geometry, which has been titled “Karbandi.” The most important and highly acclaimed feature of Karbandi is the correlation and coordination between its architectural and structural functions, which results in creating esthetic and meaningful spaces. The use of this structure is highly demanded in contemporary Persian architecture, but very little information about historical techniques survives to the present day and accordingly, there are ambiguities about its drawing and geometric design. Therefore, this research aims at discovering geometric relationships and principles of Karbandi to regulate and facilitate its design process in contemporary architecture. Toward this end, its historical samples were analyzed and their geometric features were found. As a consequence, the connection distance of dividing points on the circle is an important parameter for creating various types of Karbandi on a base. For instance, the height of a Karbandi and its elaboration are directly related to the connection distance. In addition, it was clarified that the height of a Karbandi and the size of its Shamseh are in an inverse relationship. Finally, a comprehensive classification was presented based on found geometric features.

Application-based principles of islamic geometric patterns; state-of-the-art, and future trends in computer science/technologies: a review

“…Mohammadi et al [178] offered a solution to broaden karbandi's use over irregular geometry, showing how to calculate and implement karbandi geometry in irregular bases under specific conditions. The same authors [99] discovered geometric relationships and principles of karbandi to regulate and facilitate its design process in contemporary architecture. Maleki and Woodbury [34] developed the geometric constraints of rasmibandi, representing the location of the defining points of a dome.…”

“…Master Lorzadeh , one of the last of his generation with a link to eighteenth-century traditions of master builders, believed in the drawing of karbandi based on the division of semicircle by the radiuses from the center of the span and its extension on the rectangular surface [22]. Other scholars believe that "the plan of an n-sided karbandi is on the basis of dividing a circle into n equal sectors and drawing intersecting equal chords between the dividing points [97][98][99]. Then, the final pattern is formed based on the funicular transforming of any lines of initial patterns, producing lattice structure or ribbed vaults [100].…”

“…There is a relationship between the height of karbandi and the size of shamseh. [99]. Moreover, there is a correlation and coordination between architectural and structural functions in karbandi, causing aesthetic and meaningful spaces with structural performance [101,102].…”

Symmetry Relations in Crossed-Arch Domes

“…Over the last couple of decades there has been an effort to study and fully inventory these existing structures in the western world, as their number is not very high (Fuentes González, 2013 Huerta, 2010;Galdieri, 1983;Sakkal, 1995-97;Velázquez Bosco, 1894). In Iran, where the quantity of karbandies is difficult to calculate, the study has followed the path of discovery/definition of systematization rules of geometric design (Mohamadianmansoor et al, 2012;Mohammadi et al, 2018;Mohammadi et al, 2019), denomination (Naeeni et al, 2017;Pour Ahmadi, 2014), and construction (Ainechi et al, 2019;Nazari, 2021). The variations are so many, dependent on masters and regions, that even the systematization is a difficult task.…”

Configuration processing and construction of large-span karbandi vaults: a case of the karbandi vaulting of Haj-Mohammad-Qoli Timche in Tabriz Historic Bazaar

“…, 2013). Such a structure is generated by intersecting several arches with a harmonic stellar geometry (Nava'i and Haji Qassemi, 2011), which is considered as a traditional kind of lattice space dome (Amjad Mohammadi et al. , 2019).…”