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A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern

A study on the construction technology of the Seljuk minarets in Isfahan with focus on their... Curved and Layer. Struct. 2022; 9:13–24 Research Article Ali Safaeianpour and Nima Valibeig* A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern https://doi.org/10.1515/cls-2022-0002 of the minaret’s overall shape, the brick patterns are con- Received Dec 23, 2020; accepted Mar 09, 2021 structed on a greater surface area at the bottom compared to the available surface at the upper parts. In other words, Abstract: Using decorative elements is an inseparable as- the cross-section diameter is gradually decreased during pect of Iranian architecture. Architectural ornaments in the construction; consequently, the surface area will be many buildings, including the minarets, represent the ar- reduced as well. As a result, in projecting these brickworks chitect’s craftsmanship. As such, the minarets in Isfahan on a shrinking surface, retaining the geometric integrity of have different types of brickwork ornamentations, such these patterns could become very challenging. Neverthe- as 90-degree herringbone (Khofteh-Rasteh), basket weave less, even though the cross-section diameter is decreasing, bond (Hasiri), and other complex types. Additionally, the the overall design should cover the exterior façade com- highest minarets are usually constructed in a truncated pletely. Similarly, in implementing these patterns on the conical shape to reduce their overall weight and ameliorate minaret, the pattern should be put together around the sur- their stability against the wind, and lateral forces. There- face accurately and appropriately; that is, an implemented fore, while the geometric integrity of brickwork patterns design without overlapping parts at different height levels. should be maintained, all the ornamentations are applied Besides, the integrity of geometric order in the implemented on a shrinking surface area. However, the practical solu- patterns should be successfully maintained. tions for the construction processes in these structures Therefore, this study aims to answer these questions: haven’t been sufficiently investigated. Hence, this study – How a two-dimensional brickwork pattern on the aims to explore the methods of brickwork projection on minaret’s three-dimensional curved surface could be the minarets and analyse the changes in girih patterns at implemented without losing the integrity of geomet- different height levels. Accordingly, after surveying the se- ric order? lected single minarets in Isfahan, they were modeled using – What practical solutions have been developed to drafting software applications and then analysed. maintain the geometric integrity on the minaret’s Keywords: minarets of Isfahan, use of brick tile (girih) on cone-shaped surface? curved façade, geometry in architecture, brickwork, geo- metric pattern 1.1 Research background Most previous studies about girih patterns are concerned 1 Introduction with two-dimensional planes. So, this study is one of the earliest endeavors in analysing and addressing the chal- The minaret is an architectural type with symbolic signif- lenges regarding the implementation of these patterns in icance in the Middle East. The exterior surface is usually three-dimensional structures and the practical solutions ornamented with brickwork patterns that are designed thereof. In previous studies about the application of girih in through mathematical and geometric calculations. Because brickwork and the architectural geometry, traditional crafts- people (such as Lorzadeh, Maher-ul-Naghsh, and Sha’rbaf) and architects (such as Pirniya and Bozorgmehri) have dis- Ali Safaeianpour: Department of Urban and Art University, Art University, Isfahan, Iran cussed the implementation of girih patterns thoroughly [1]. *Corresponding Author: Nima Valibeig: Department of Urban In other studies, girih patterns have been seen concerning and Architectural Conservation, Art University, Isfahan, Iran E-mail: connections to mathematics [2]. Moreover, the similarity of n.valibeig@aui.ac.ir Open Access. © 2022 Safaeianpour and Valibeig, published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License 14 | Safaeianpour and Valibeig geometry used in girih patterns and fractals has been dis- among all the existing single minarets in the former Seljuk cussed as well. Due to the repetitive and indefinite nature of capital where the perfection of brickwork was achieved. The the pattern, nature has been recognized as a source of inspi- data collection method has been through architectural sur- ration in designing girih patterns [3]. Accordingly, different veying and field research, and the accuracy was achieved types of girih have been categorized into two groups based through a brick-by-brick architectural survey at different on their drawing method: those designed traditionally, or height levels in both minarets with simple brickworks and by modern means [4]. As such, some studies about Islamic those with intricate girih patterns. All data were analysed geometric patterns discussed the method of designing girih and modelled through computer-aided design and drafting patterns through angled lines and circles [5, 6]. In another software applications: AutoCAD 2017 (Autodesk, Inc.) and study, apart from explaining the implementation of girih on Rhino v5.0, 2017 (Robert McNeel & Associates). After draw- different minarets, the brick-dimensions were mentioned ing the two-dimensional and three-dimensional models in [7]. In another study, the dynamic behavior of columns was AutoCAD, the construction procedure at different height analysed [8]. Even though exploring the diverse methods levels was modeled in Rhino application and then anal- and their practical implementations have been in the fo- ysed. cus of many studies, the practical solutions to design girih patterns in the minaret’s brickwork as well as making es- sential changes in these structures are being addressed 2 Girih for the first time in the present study; correspondingly, the changes from the bottom of the minaret to its top (A to B) Girih, otherwise called gereh (meaning ‘knot’ in Parsi), con- or from its exterior surface to the interior one (C to B) will sists of different Persianate geometric patterns made by a be investigated in this article (Figure 1). composition of oblique or orthographical interlacing lines that are aligned in a certain order [9]. Girih patterns have been the subject of great interest among many researchers and foreign tourists. Therefore, in quite a huge number of historic manuscripts and palimpsests, we encounter some information about these art-forms [10]. The designed pat- terns can be extended by connecting different girih patterns [4]. As an ornamentation style to cover the façade, girih pat- terns can be designed either within a fixed frame or could be developed further inside the existing girih pieces [11]. Girih could also be constructed with different materials in archi- tecture and can be seen in wood, plasterwork, tilework, and brickwork decorations [12]. Based on the material used, the implementation of girih could either be flat or embossed; for instance, by the horizontal displacement of the brick, the girih pattern can be raised above the main surface [13]. So far, different design methods have been suggested for implementing elaborate girih patterns on flat surfaces [14]; but, the focus of this research remains on the implemen- tation of girih on 3-D planes. In other words, the usage of girih in the brickwork ornamentations on minarets with truncated conical shapes will be analysed here. Figure 1: Pattern changes from the bottom to the top; the difference. 2.1 Girih on a flat surface Even though the simplest method for drawing a girih and 1.2 Research method implementing it on a surface is to create it on a flat 2-D plane, all design methods have one shared component that In this study, some of the minarets in Isfahan with a cylindri- is called design grids. These grids are a set of lines usually cal or a truncated cone form were selected as case studies A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern | 15 prepared in two different arrangements: the ‘polar grid’ and like the curvature in the sphere or a saddle surface. This ‘polygonal grid’ subdivisions [15]. Even though there are research, however, focuses on different types of girih pat- many possible ways to draw girih patterns, the emphasis is terns designed and implemented on surfaces with simple mainly on the usage of either the central or axial symmetry; one-directional curvatures. nevertheless, a combined method could be used as well [5]. As seen in Figure 2, new elaborate designs can be created by dividing the girih pieces and creating new girih patterns inside the previous ones [16]. Figure 3: Example of girih patterns with 9-pointed, 10-pointed, 11-pointed, and 12-pointed stars [12]. Figure 2: Example of new design subdivisions in girih [16]. Figure 4: Repeating the main pattern on a hyperbolic plane [19]. 2.2 Girih on a curved surface Any girih pattern with only one regular concave polygon (Shamseh or star) would be called ‘singular-ground’ or ‘tak- zamineh’; while those with multiple stars are ‘multiple- ground’ or ‘provisional girih patterns’, respectively called 2.3 Girih on a cylindrical surface ‘chand-zamineh’ or ‘dast-gardan’ [4]. The former type is simple and regular, whereas the latter is complicated and There are two different ways to draw a girih on a cylindrical irregular (see Figure 3). Notably, in the multiple-ground volume: group, if the star polygons have a similar number of points, a) Drawing on an unrolled 2-D cylinder: The unrolled the geometric order can be maintained easily [17]. Kaplan, surface of a cylinder has a rectangular shape. To draw a and Salesin, have stated that “as curvature decreases and girih pattern on the cylindrical surface, it would be needed we move from the sphere to the Euclidean plane to the hy- to model that on a rectangle with the length and width perbolic plane, the same underlying pattern accommodates corresponding to the circumference of the cross-section stars with ever-larger numbers of points” [18]. As illustrated circle and the height of the cylinder; then, this rectangular in Figure 4–5, the repeating pattern in a hyperbolic plane surface will be rolled back to form a cylinder again (Figure (or the Euclidean plane or the sphere) includes congruent 6). copies of a basic sub-pattern or motif [19]. b) Drawing on a 3-D cylindrical volume: To draw the These curved surfaces may have a simple curvature girih pattern in this method, first, a set of grid circles is that tilts towards one direction; such as in the cylindrical drawn on the cylindrical shape. Subsequently, the girih will or conical surfaces. Otherwise, they may have a double be drawn with the help of these grids (Figure 7). The role curvature that would lean towards two different directions, 16 | Safaeianpour and Valibeig Figure 6: Projecting patterns on an unrolled cylindrical surface [20]. they would make the mosque’s location discoverable from the distance [21]. The minarets near religious buildings are built either singularly or in pairs [22]. However, the number of minarets may vary in other places like Sultanieh Dome in Zanjan or Hagia Sophia in Istanbul. Moreover, each minaret consists of various structural elements such as the base, shaft, cap, and crown. In general, based on their formal structure, minarets can be divided into three different cate- gories of cylindrical, truncated conical, or prismatic forms [23]. Also, they are usually embellished with various types Figure 5: Example of projecting Islamic patterns on a sphere, Eu- of simple linear ornamentations or complicated and intri- clidean, and hyperbolic planes [18]. cate girih patterns. Minarets have unique characteristics in structural be- havior, and various items affect minaret’s dynamic re- of these grids is, thus, to make the drawings geometrically sponses, such as minaret cross-section diameter. The more accurate. greater diameter in cross-section causes the less lateral In both methods, the ratio between the dimensions of dynamic response of the minaret [24]. Moreover, minarets the girih pattern and the cylinder’s radius should be con- need more weight in the lower cross-sections to have a sidered [20]. The method selection depends on factors such more stable response subjected to lateral forces [25]. Hence, as the designer’s skill or the type of design. For instance, minarets are usually constructed in a truncated conical the second method is suitable for designing the patterns in shape. circular grounds. 3.1 Brick minaret 2.4 Girih on a truncated conical surface Brick is one of the most commonly used materials in the In projecting a girih on a truncated cone-shaped minaret, construction of minarets. In Middle East, it has been used it is important to retain the geometric order because of in most buildings due to the availability of this material the diameter of the cross-section, and subsequently, the as well as its adaptability to the regional climate [26]. In exterior surface area is gradually reduced in different cross- this region, particularly the Seljuk period, was the pinnacle sections levels (see Figure 1). of art and architecture, especially in developing stunning brickwork decorations [27]. The architecture of this era is marked with stunning brickwork on the building façades 3 Minaret [28]; as such, the buildings that are attributed to this period are covered with bewildering brickwork patterns that prove Minarets are mostly tall tower structures with a circular the incredible skill of its artists and architect [29]. Addition- plan that are usually constructed near a mosque, or where ally, the brick pieces that were used in the load-bearing A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern | 17 Figure 7: Method of drawing the patterns on a cylinder using a compass [20]. elements were usually molded with dimensions between these models, the patterns are compressed. To further inves- 20–40 cm, and they were cut into smaller pieces to suit the tigate this process, those minarets in the Isfahan Province architect’s need for different height levels [26]. that were attributed to the Seljuk period were chosen as case studies so their patterns could be photographed and analysed for this research. 3.2 Girih in the truncated conical Seljuk minarets 3.2.1 Girih in the Chehel-Dokhtaran minaret Usually, higher minarets are constructed in a truncated The Chehel-Dokhtaran minaret is known as the first minaret cone-shaped form (Tables 1 and 2) to achieve higher sta- in Isfahan that contains an inscription dating back to the bility against the wind force and seismic activities [23]. 11th century AD (Figures 8a and 8b). The surface of this There are different types of brickwork on minarets. One of truncated cone-shaped minaret is covered with brickwork the main techniques of constructing brickwork is to make decorations. brick reliefs by horizontally displacing some bricks from However, since the difference between the cross- the main surface [30]. In such minarets, the patterns should section diameters at the top and bottom, respectively, 2.30 be changed due to the decrease of the circumference circle. m and 2.90 m, is negligible [26], the minaret’s outlook re- As we move from the bottom to top, and the cross-section’s sembles the minarets with a cylindrical shape. In Table 3 diameter decreases, the pattern would inevitably and grad- the changes of patterns on this minaret are analyzed. ually become more compressed (Tables 1–5; also Figure 1); In this minaret, both types I and II solutions are applied whether the girih is simple or intricate, this change may dis- to retain the geometric integrity in the patterns. The belt turb the overall integrity of the geometric order in all types course between the two frames containing different girih of brickwork. Therefore, to retain the geometric homogene- patterns illustrates the usage of the second solution. Nev- ity, various solutions have been applied by the architects. ertheless, due to the considerable height of this minaret, These solutions mostly consist of either the change in the this solution has not been sufficient. Therefore, in the struc- shape and size of the bricks or modifying the pattern type. ture’s upper levels, brick conversion (type I solution) is For the first practical solution (type I), brick shapes observed are converted from rectangular pieces to trapezoid ones at the upper levels of the minaret by cutting the bricks one by one; thus, the geometric order will be retained as the 3.2.2 Girih in the minarets of Masjed-Ali and Sareban in cross-section diameter is reduced. Moreover, a more stable Isfahan shape will be constructed as well (Tables 1–5). In the second solution (type II), the architect would The minarets of Masjed-Ali and Sareban (Figures 9a and change the design at the higher levels, so that the brick 9b) are both attributed to the Seljuk era. The minaret of cutting would not become necessary. Hence, using this Ali mosque or Masjed-Ali minaret is constructed near the method involves a simpler practical implementation. Jameh mosque in Isfahan. The Sareban minaret is situated As illustrated in Tables 1 and 2, the change process close to the northern parts of the Jubareh district in the city in the geometric patterns is shown, for a cylinder, a trun- of Isfahan. In both case studies, the usage of type I solution cated cone (resembling the minaret’s form), and a cone. Analysing these pictures indicates that in the upper parts of 18 | Safaeianpour and Valibeig Table 1: The change process in simple brickwork pattern modeled on different 3-D shapes (cylinder, truncated cone, and cone). No Title Cylinder Truncated cone Cone 1 Unrolled 2-D model 2 2-D model projection to 3-D 3 Brick structure A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern | 19 Table 2: The change process in 90-degree herringbone brickwork pattern modeled on different 3-D shapes (cylinder, truncated cone, and cone). No Title Cylinder Truncated cone Cone 1 Unrolled 2-D model 2 2-D model projection to 3-D 3 Brick structure 20 | Safaeianpour and Valibeig Table 3: The change process in girih pattern of the brickwork in the Chehel-Dokhtaran minaret modeled on different 3-D shapes (cylinder, truncated cone, and cone). No Title Cylinder Truncated cone Cone 1 Unrolled 2-D model 2 2-D model projection to 3-D Table 4: The change process in girih pattern of the brickwork in the Sareban and Masjed-Ali minarets modeled on different 3-D shapes (cylinder, truncated cone, and cone). No Title Cylinder Truncated cone Cone 1 Unrolled 2-D model 2 Brick structure A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern | 21 (a) (b) Figure 9: Minarets in the city of Isfahan; a) Sareban b) Masjed-Ali. (a) Figure 10: The conversion of bricks from a rectangular shape to a trapezoid one. 3.2.3 Girih in the Golpayegan minaret Golpayegan is a town in Isfahan Province, located at the North-West of Isfahan city. The brick minaret in Golpayegan (b) is also attributed to the Seljuk period (Figure 11) and has Figure 8: The brickwork ornamentations on Chehel-Dokhtaran considerable brickwork decorations, among which two Minaret a) overall view; b) detailed view. Kufic inscription panels are spectacular. The minaret consists of two main parts: a prismatic shape at the bottom, and a portion resembling a truncated is seen. The geometric patterns on the upper side of the cone in which all types of girih adjustments can be observed minaret do not seem to change. (Table 5). The results of the field survey in this study revealed In this minaret, type II solution has been applied; that the brick blocks were most probably cut into the de- that is, to project this pattern, not only the brick shape sired shapes and smaller sizes; so that, despite the gradual is changed at different height levels, but also in the up- decrease of cross-section dimensions, the geometric pat- per parts of this minaret, the joint width between the brick tern retains its overall integrity; the cuts convert the bricks blocks is reduced as well. from a rectangular shape to a trapezoid form (Figure 10). Also, the larger dimensions of girih pieces (Mohreh) could be another reason as to why the architect did not change the patterns in the upper parts (Table 4). 22 | Safaeianpour and Valibeig Table 5: The change process in girih pattern of the brickwork in the Sareban and Masjed-Ali minarets modeled on different 3-D shapes (cylinder, truncated cone, and cone). No Title Cylinder Truncated cone Cone 1 Unrolled 2-D model 2 2-D model projection to 3-D 3 Brick structure A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern | 23 spectator observes the minaret from the ground level, any disintegration and lack of perfect geometric order remain almost unnoticeable. All in all, this study has provided new explanations regarding the practical solutions of implementing girih pat- terns on the minaret’s curved surface. Apart from these findings, it is suggested to use the method and process of this analysis in similar studies on other minarets and struc- tures with elements having two-directional curved planes, such as domes. Funding information: The authors state no funding in- volved. Author contributions: All authors have accepted responsi- bility for the entire content of this manuscript and approved its submission. Conflict of interest: The authors state no conflict of inter- est. Figure 11: The Golpayegan minaret. 4 Conclusion References The truncated cones have a smaller diameter at the top com- [1] Valibeig N, Tavakoli S, Khodadadi N. Form and Geometry in Dec- orative Tile Work in Khayyatha Mosque, Isfahan. Europ Online J pared to the bottom of the shape. To implement geometric Nat Soc Sci: Proc. 2015;3(4):534-546. patterns on these shapes, if the outer cross-section diameter [2] Özdural A. Mathematics and arts: Connections between the- at the top has little difference from the diameter at the bot- ory and practice in the medieval Islamic world. Historia Math. tom, simple solutions were applied. Therefore, reducing the 2000;27(2):171-201. distance between the horizontal brick rows in higher levels [3] Balilian Asl L, Sattar-Zadeh D, Khorshidian S, Nouri M. The Study of the Characteristics of Geometrical Knots in Islamic Decora- may keep the geometric integrity in the façade. Yet, in some tions from the Viewpoint of Fractal Geometry. J ICAS: Iran Islamic minarets, the difference of cross-section diameters at the City Studies. 2011;2(6):83-95. top and bottom of the minaret is not negligible. Hence, the [4] Nourian Y, Kasraei MH. A Comparison of Traditional Knot implementation of girih may have required other solutions. to Contemporary Islamic Patterns;Focusing on their Applica- Architects and skilled craftspeople applied two main tions in Contemporary Architecture. 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Bridges: Math- ematics, Music, Art, Architecture, Education, Culture, Jyvaskylla, Finland; 2016:331-336. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Curved and Layered Structures de Gruyter

A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern

Curved and Layered Structures , Volume 9 (1): 12 – Jan 1, 2022

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Curved and Layer. Struct. 2022; 9:13–24 Research Article Ali Safaeianpour and Nima Valibeig* A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern https://doi.org/10.1515/cls-2022-0002 of the minaret’s overall shape, the brick patterns are con- Received Dec 23, 2020; accepted Mar 09, 2021 structed on a greater surface area at the bottom compared to the available surface at the upper parts. In other words, Abstract: Using decorative elements is an inseparable as- the cross-section diameter is gradually decreased during pect of Iranian architecture. Architectural ornaments in the construction; consequently, the surface area will be many buildings, including the minarets, represent the ar- reduced as well. As a result, in projecting these brickworks chitect’s craftsmanship. As such, the minarets in Isfahan on a shrinking surface, retaining the geometric integrity of have different types of brickwork ornamentations, such these patterns could become very challenging. Neverthe- as 90-degree herringbone (Khofteh-Rasteh), basket weave less, even though the cross-section diameter is decreasing, bond (Hasiri), and other complex types. Additionally, the the overall design should cover the exterior façade com- highest minarets are usually constructed in a truncated pletely. Similarly, in implementing these patterns on the conical shape to reduce their overall weight and ameliorate minaret, the pattern should be put together around the sur- their stability against the wind, and lateral forces. There- face accurately and appropriately; that is, an implemented fore, while the geometric integrity of brickwork patterns design without overlapping parts at different height levels. should be maintained, all the ornamentations are applied Besides, the integrity of geometric order in the implemented on a shrinking surface area. However, the practical solu- patterns should be successfully maintained. tions for the construction processes in these structures Therefore, this study aims to answer these questions: haven’t been sufficiently investigated. Hence, this study – How a two-dimensional brickwork pattern on the aims to explore the methods of brickwork projection on minaret’s three-dimensional curved surface could be the minarets and analyse the changes in girih patterns at implemented without losing the integrity of geomet- different height levels. Accordingly, after surveying the se- ric order? lected single minarets in Isfahan, they were modeled using – What practical solutions have been developed to drafting software applications and then analysed. maintain the geometric integrity on the minaret’s Keywords: minarets of Isfahan, use of brick tile (girih) on cone-shaped surface? curved façade, geometry in architecture, brickwork, geo- metric pattern 1.1 Research background Most previous studies about girih patterns are concerned 1 Introduction with two-dimensional planes. So, this study is one of the earliest endeavors in analysing and addressing the chal- The minaret is an architectural type with symbolic signif- lenges regarding the implementation of these patterns in icance in the Middle East. The exterior surface is usually three-dimensional structures and the practical solutions ornamented with brickwork patterns that are designed thereof. In previous studies about the application of girih in through mathematical and geometric calculations. Because brickwork and the architectural geometry, traditional crafts- people (such as Lorzadeh, Maher-ul-Naghsh, and Sha’rbaf) and architects (such as Pirniya and Bozorgmehri) have dis- Ali Safaeianpour: Department of Urban and Art University, Art University, Isfahan, Iran cussed the implementation of girih patterns thoroughly [1]. *Corresponding Author: Nima Valibeig: Department of Urban In other studies, girih patterns have been seen concerning and Architectural Conservation, Art University, Isfahan, Iran E-mail: connections to mathematics [2]. Moreover, the similarity of n.valibeig@aui.ac.ir Open Access. © 2022 Safaeianpour and Valibeig, published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License 14 | Safaeianpour and Valibeig geometry used in girih patterns and fractals has been dis- among all the existing single minarets in the former Seljuk cussed as well. Due to the repetitive and indefinite nature of capital where the perfection of brickwork was achieved. The the pattern, nature has been recognized as a source of inspi- data collection method has been through architectural sur- ration in designing girih patterns [3]. Accordingly, different veying and field research, and the accuracy was achieved types of girih have been categorized into two groups based through a brick-by-brick architectural survey at different on their drawing method: those designed traditionally, or height levels in both minarets with simple brickworks and by modern means [4]. As such, some studies about Islamic those with intricate girih patterns. All data were analysed geometric patterns discussed the method of designing girih and modelled through computer-aided design and drafting patterns through angled lines and circles [5, 6]. In another software applications: AutoCAD 2017 (Autodesk, Inc.) and study, apart from explaining the implementation of girih on Rhino v5.0, 2017 (Robert McNeel & Associates). After draw- different minarets, the brick-dimensions were mentioned ing the two-dimensional and three-dimensional models in [7]. In another study, the dynamic behavior of columns was AutoCAD, the construction procedure at different height analysed [8]. Even though exploring the diverse methods levels was modeled in Rhino application and then anal- and their practical implementations have been in the fo- ysed. cus of many studies, the practical solutions to design girih patterns in the minaret’s brickwork as well as making es- sential changes in these structures are being addressed 2 Girih for the first time in the present study; correspondingly, the changes from the bottom of the minaret to its top (A to B) Girih, otherwise called gereh (meaning ‘knot’ in Parsi), con- or from its exterior surface to the interior one (C to B) will sists of different Persianate geometric patterns made by a be investigated in this article (Figure 1). composition of oblique or orthographical interlacing lines that are aligned in a certain order [9]. Girih patterns have been the subject of great interest among many researchers and foreign tourists. Therefore, in quite a huge number of historic manuscripts and palimpsests, we encounter some information about these art-forms [10]. The designed pat- terns can be extended by connecting different girih patterns [4]. As an ornamentation style to cover the façade, girih pat- terns can be designed either within a fixed frame or could be developed further inside the existing girih pieces [11]. Girih could also be constructed with different materials in archi- tecture and can be seen in wood, plasterwork, tilework, and brickwork decorations [12]. Based on the material used, the implementation of girih could either be flat or embossed; for instance, by the horizontal displacement of the brick, the girih pattern can be raised above the main surface [13]. So far, different design methods have been suggested for implementing elaborate girih patterns on flat surfaces [14]; but, the focus of this research remains on the implemen- tation of girih on 3-D planes. In other words, the usage of girih in the brickwork ornamentations on minarets with truncated conical shapes will be analysed here. Figure 1: Pattern changes from the bottom to the top; the difference. 2.1 Girih on a flat surface Even though the simplest method for drawing a girih and 1.2 Research method implementing it on a surface is to create it on a flat 2-D plane, all design methods have one shared component that In this study, some of the minarets in Isfahan with a cylindri- is called design grids. These grids are a set of lines usually cal or a truncated cone form were selected as case studies A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern | 15 prepared in two different arrangements: the ‘polar grid’ and like the curvature in the sphere or a saddle surface. This ‘polygonal grid’ subdivisions [15]. Even though there are research, however, focuses on different types of girih pat- many possible ways to draw girih patterns, the emphasis is terns designed and implemented on surfaces with simple mainly on the usage of either the central or axial symmetry; one-directional curvatures. nevertheless, a combined method could be used as well [5]. As seen in Figure 2, new elaborate designs can be created by dividing the girih pieces and creating new girih patterns inside the previous ones [16]. Figure 3: Example of girih patterns with 9-pointed, 10-pointed, 11-pointed, and 12-pointed stars [12]. Figure 2: Example of new design subdivisions in girih [16]. Figure 4: Repeating the main pattern on a hyperbolic plane [19]. 2.2 Girih on a curved surface Any girih pattern with only one regular concave polygon (Shamseh or star) would be called ‘singular-ground’ or ‘tak- zamineh’; while those with multiple stars are ‘multiple- ground’ or ‘provisional girih patterns’, respectively called 2.3 Girih on a cylindrical surface ‘chand-zamineh’ or ‘dast-gardan’ [4]. The former type is simple and regular, whereas the latter is complicated and There are two different ways to draw a girih on a cylindrical irregular (see Figure 3). Notably, in the multiple-ground volume: group, if the star polygons have a similar number of points, a) Drawing on an unrolled 2-D cylinder: The unrolled the geometric order can be maintained easily [17]. Kaplan, surface of a cylinder has a rectangular shape. To draw a and Salesin, have stated that “as curvature decreases and girih pattern on the cylindrical surface, it would be needed we move from the sphere to the Euclidean plane to the hy- to model that on a rectangle with the length and width perbolic plane, the same underlying pattern accommodates corresponding to the circumference of the cross-section stars with ever-larger numbers of points” [18]. As illustrated circle and the height of the cylinder; then, this rectangular in Figure 4–5, the repeating pattern in a hyperbolic plane surface will be rolled back to form a cylinder again (Figure (or the Euclidean plane or the sphere) includes congruent 6). copies of a basic sub-pattern or motif [19]. b) Drawing on a 3-D cylindrical volume: To draw the These curved surfaces may have a simple curvature girih pattern in this method, first, a set of grid circles is that tilts towards one direction; such as in the cylindrical drawn on the cylindrical shape. Subsequently, the girih will or conical surfaces. Otherwise, they may have a double be drawn with the help of these grids (Figure 7). The role curvature that would lean towards two different directions, 16 | Safaeianpour and Valibeig Figure 6: Projecting patterns on an unrolled cylindrical surface [20]. they would make the mosque’s location discoverable from the distance [21]. The minarets near religious buildings are built either singularly or in pairs [22]. However, the number of minarets may vary in other places like Sultanieh Dome in Zanjan or Hagia Sophia in Istanbul. Moreover, each minaret consists of various structural elements such as the base, shaft, cap, and crown. In general, based on their formal structure, minarets can be divided into three different cate- gories of cylindrical, truncated conical, or prismatic forms [23]. Also, they are usually embellished with various types Figure 5: Example of projecting Islamic patterns on a sphere, Eu- of simple linear ornamentations or complicated and intri- clidean, and hyperbolic planes [18]. cate girih patterns. Minarets have unique characteristics in structural be- havior, and various items affect minaret’s dynamic re- of these grids is, thus, to make the drawings geometrically sponses, such as minaret cross-section diameter. The more accurate. greater diameter in cross-section causes the less lateral In both methods, the ratio between the dimensions of dynamic response of the minaret [24]. Moreover, minarets the girih pattern and the cylinder’s radius should be con- need more weight in the lower cross-sections to have a sidered [20]. The method selection depends on factors such more stable response subjected to lateral forces [25]. Hence, as the designer’s skill or the type of design. For instance, minarets are usually constructed in a truncated conical the second method is suitable for designing the patterns in shape. circular grounds. 3.1 Brick minaret 2.4 Girih on a truncated conical surface Brick is one of the most commonly used materials in the In projecting a girih on a truncated cone-shaped minaret, construction of minarets. In Middle East, it has been used it is important to retain the geometric order because of in most buildings due to the availability of this material the diameter of the cross-section, and subsequently, the as well as its adaptability to the regional climate [26]. In exterior surface area is gradually reduced in different cross- this region, particularly the Seljuk period, was the pinnacle sections levels (see Figure 1). of art and architecture, especially in developing stunning brickwork decorations [27]. The architecture of this era is marked with stunning brickwork on the building façades 3 Minaret [28]; as such, the buildings that are attributed to this period are covered with bewildering brickwork patterns that prove Minarets are mostly tall tower structures with a circular the incredible skill of its artists and architect [29]. Addition- plan that are usually constructed near a mosque, or where ally, the brick pieces that were used in the load-bearing A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern | 17 Figure 7: Method of drawing the patterns on a cylinder using a compass [20]. elements were usually molded with dimensions between these models, the patterns are compressed. To further inves- 20–40 cm, and they were cut into smaller pieces to suit the tigate this process, those minarets in the Isfahan Province architect’s need for different height levels [26]. that were attributed to the Seljuk period were chosen as case studies so their patterns could be photographed and analysed for this research. 3.2 Girih in the truncated conical Seljuk minarets 3.2.1 Girih in the Chehel-Dokhtaran minaret Usually, higher minarets are constructed in a truncated The Chehel-Dokhtaran minaret is known as the first minaret cone-shaped form (Tables 1 and 2) to achieve higher sta- in Isfahan that contains an inscription dating back to the bility against the wind force and seismic activities [23]. 11th century AD (Figures 8a and 8b). The surface of this There are different types of brickwork on minarets. One of truncated cone-shaped minaret is covered with brickwork the main techniques of constructing brickwork is to make decorations. brick reliefs by horizontally displacing some bricks from However, since the difference between the cross- the main surface [30]. In such minarets, the patterns should section diameters at the top and bottom, respectively, 2.30 be changed due to the decrease of the circumference circle. m and 2.90 m, is negligible [26], the minaret’s outlook re- As we move from the bottom to top, and the cross-section’s sembles the minarets with a cylindrical shape. In Table 3 diameter decreases, the pattern would inevitably and grad- the changes of patterns on this minaret are analyzed. ually become more compressed (Tables 1–5; also Figure 1); In this minaret, both types I and II solutions are applied whether the girih is simple or intricate, this change may dis- to retain the geometric integrity in the patterns. The belt turb the overall integrity of the geometric order in all types course between the two frames containing different girih of brickwork. Therefore, to retain the geometric homogene- patterns illustrates the usage of the second solution. Nev- ity, various solutions have been applied by the architects. ertheless, due to the considerable height of this minaret, These solutions mostly consist of either the change in the this solution has not been sufficient. Therefore, in the struc- shape and size of the bricks or modifying the pattern type. ture’s upper levels, brick conversion (type I solution) is For the first practical solution (type I), brick shapes observed are converted from rectangular pieces to trapezoid ones at the upper levels of the minaret by cutting the bricks one by one; thus, the geometric order will be retained as the 3.2.2 Girih in the minarets of Masjed-Ali and Sareban in cross-section diameter is reduced. Moreover, a more stable Isfahan shape will be constructed as well (Tables 1–5). In the second solution (type II), the architect would The minarets of Masjed-Ali and Sareban (Figures 9a and change the design at the higher levels, so that the brick 9b) are both attributed to the Seljuk era. The minaret of cutting would not become necessary. Hence, using this Ali mosque or Masjed-Ali minaret is constructed near the method involves a simpler practical implementation. Jameh mosque in Isfahan. The Sareban minaret is situated As illustrated in Tables 1 and 2, the change process close to the northern parts of the Jubareh district in the city in the geometric patterns is shown, for a cylinder, a trun- of Isfahan. In both case studies, the usage of type I solution cated cone (resembling the minaret’s form), and a cone. Analysing these pictures indicates that in the upper parts of 18 | Safaeianpour and Valibeig Table 1: The change process in simple brickwork pattern modeled on different 3-D shapes (cylinder, truncated cone, and cone). No Title Cylinder Truncated cone Cone 1 Unrolled 2-D model 2 2-D model projection to 3-D 3 Brick structure A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern | 19 Table 2: The change process in 90-degree herringbone brickwork pattern modeled on different 3-D shapes (cylinder, truncated cone, and cone). No Title Cylinder Truncated cone Cone 1 Unrolled 2-D model 2 2-D model projection to 3-D 3 Brick structure 20 | Safaeianpour and Valibeig Table 3: The change process in girih pattern of the brickwork in the Chehel-Dokhtaran minaret modeled on different 3-D shapes (cylinder, truncated cone, and cone). No Title Cylinder Truncated cone Cone 1 Unrolled 2-D model 2 2-D model projection to 3-D Table 4: The change process in girih pattern of the brickwork in the Sareban and Masjed-Ali minarets modeled on different 3-D shapes (cylinder, truncated cone, and cone). No Title Cylinder Truncated cone Cone 1 Unrolled 2-D model 2 Brick structure A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern | 21 (a) (b) Figure 9: Minarets in the city of Isfahan; a) Sareban b) Masjed-Ali. (a) Figure 10: The conversion of bricks from a rectangular shape to a trapezoid one. 3.2.3 Girih in the Golpayegan minaret Golpayegan is a town in Isfahan Province, located at the North-West of Isfahan city. The brick minaret in Golpayegan (b) is also attributed to the Seljuk period (Figure 11) and has Figure 8: The brickwork ornamentations on Chehel-Dokhtaran considerable brickwork decorations, among which two Minaret a) overall view; b) detailed view. Kufic inscription panels are spectacular. The minaret consists of two main parts: a prismatic shape at the bottom, and a portion resembling a truncated is seen. The geometric patterns on the upper side of the cone in which all types of girih adjustments can be observed minaret do not seem to change. (Table 5). The results of the field survey in this study revealed In this minaret, type II solution has been applied; that the brick blocks were most probably cut into the de- that is, to project this pattern, not only the brick shape sired shapes and smaller sizes; so that, despite the gradual is changed at different height levels, but also in the up- decrease of cross-section dimensions, the geometric pat- per parts of this minaret, the joint width between the brick tern retains its overall integrity; the cuts convert the bricks blocks is reduced as well. from a rectangular shape to a trapezoid form (Figure 10). Also, the larger dimensions of girih pieces (Mohreh) could be another reason as to why the architect did not change the patterns in the upper parts (Table 4). 22 | Safaeianpour and Valibeig Table 5: The change process in girih pattern of the brickwork in the Sareban and Masjed-Ali minarets modeled on different 3-D shapes (cylinder, truncated cone, and cone). No Title Cylinder Truncated cone Cone 1 Unrolled 2-D model 2 2-D model projection to 3-D 3 Brick structure A study on the construction technology of the Seljuk minarets in Isfahan with focus on their geometric brick pattern | 23 spectator observes the minaret from the ground level, any disintegration and lack of perfect geometric order remain almost unnoticeable. All in all, this study has provided new explanations regarding the practical solutions of implementing girih pat- terns on the minaret’s curved surface. Apart from these findings, it is suggested to use the method and process of this analysis in similar studies on other minarets and struc- tures with elements having two-directional curved planes, such as domes. Funding information: The authors state no funding in- volved. Author contributions: All authors have accepted responsi- bility for the entire content of this manuscript and approved its submission. Conflict of interest: The authors state no conflict of inter- est. Figure 11: The Golpayegan minaret. 4 Conclusion References The truncated cones have a smaller diameter at the top com- [1] Valibeig N, Tavakoli S, Khodadadi N. Form and Geometry in Dec- orative Tile Work in Khayyatha Mosque, Isfahan. Europ Online J pared to the bottom of the shape. To implement geometric Nat Soc Sci: Proc. 2015;3(4):534-546. patterns on these shapes, if the outer cross-section diameter [2] Özdural A. 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Journal

Curved and Layered Structuresde Gruyter

Published: Jan 1, 2022

Keywords: minarets of Isfahan; use of brick tile (girih) on curved façade; geometry in architecture; brickwork; geometric pattern

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