17th-century Jali

Introduction

Of interest is the appearance of the Cairo tiling preceding the in situ instance of 1957 (although of course not named as such). However, instances, either as artefacts or drawings, are few and far between, and with one exception, namely of a 17th-century Mughal jali, as catalogued by Simon Ray, are (perhaps surprisingly) all of the 20th century. Although a generic Cairo tiling is easily drawn and can be described as an obvious design, it does not appear to show in history. Therefore, of particular interest in the Ray jali is the provenance, date, geometry and possible construction process. Save for the date, none of which is given by himself (and even the date has queries). However, I am a little hamstrung in this task in that my knowledge of jalis and Mughal matters in general, pre this specific instance, was next to nothing. In short, I had to quickly get up to speed on the subject, so there may very well be the odd shortcoming, if not the occasional error in such matters here. However, I have indeed striven to be my normal, exact self in the study and analysis. To this end, I now examine all these elements in detail as best I can in the circumstances. The study is in two main parts:

Part 1. Mughal Jali as Given by Simon Ray, and on Ray Himself
(a) A discussion on various aspects of the 17th-century Mughal jali in Simon Ray’s Indian & Islamic Works of Art, of 2016. This includes a transcript of the catalogue entry as well as two pictures (only two are shown in the catalogue).
(b) A look at Simon Ray as to the man and background, and see what little extra in the round may be gleaned.
(c) Simon Ray contact, or the travails…

Part 2. Examination of the Jali
(a) Inner and outer parts
(b) Angle analysis or, the determination, in principle at least, of the pentagon angles
(c) The Construction
Speculations as to a definitive pentagon - a Cordovan pentagon?

PART 1

17th-century Mughal Jali as given by Simon Ray, and on Ray Himself

(a) 17th-century Mughal jali in Indian & Islamic Works of Art, of 2016
An outstanding historical instance of the Cairo tiling, to put it mildly, is of what is said to be a 17th-century Mughal jali¹, or jaali (an Indian perforated stone screen), albeit very little is known about the background here, as an object in itself and its mathematics. This is pictured and described by Simon Ray, of the UK, a noted dealer in Indian arts (and more), in his catalogue entry in Indian & Islamic Works of Art, of 2016. For the sake of thoroughness, I show the entry in full. Italics as in the original:

Geometric Jali, India (Mughal) 17th century. Height: 158cm, Width: 93cm, Depth: 3.3cm (5 ft 2” x 3 ft x 1¼”)
A double-sided rectangular yellow sandstone jali screen, with a central carved lattice design of interlocking cartouches, surrounded by first a plain border and then a further lattice design and outer border, almost creating a jali within a jali.

The lattice carving has a single fluted incision, adding depth and texture to the panel, with the design depicting repeating interlinked hexagonal motifs which have been stretched on opposing sides, either vertically or horizontally, to create a bewildering geometric pattern. The complex design is contrasted by the thick plain border surrounding it with incised grooves to its inner and outer edges. This in turn gives way to a similar lattice framing the “inner” jali screen, only this time the hexagons have been flattened either vertically or horizontally, providing a contrast and a connection with the inner lattice.

Geometric designs in jalis such as the above are made up of patterns of permutations of simple components; notably polygons and stars, but the seemingly never-ending range of patterns can in fact be reduced to inventive manipulation of these few shapes. These Mughal patterns were common throughout the Islamic world, but can be distinguished through the expression and personality of the Mughal stonemasons and artisans.¹

I find the commentary more than a little confused:
1. Of a first reading, it is unclear as to which of the two tilings is being discussed. However (I think!), the first part refers to the Cairo tiling here in so many words, implied from the second discussion.
2. I find the description of cartouches imprecise. To me, this is not a cartouche in the normal sense² (but I may be wrong).
3. Oddly, and curiously, no mention is made of tiling, tessellations, or more specifically of pentagons in the text, although there is to the subsidiary hexagons! Tiling seems to be implied by ‘pattern’ here.
4. Peripheral to the Cairo tiling, the inner (octagon) tiling is discussed in terms of hexagons, which is a little strange, as although an underlying grid of (par)hexagons can be discerned, this is not obvious. As I show below, this is related to the jali Cairo tiling. I can only conclude here that the commentary, seemingly written by Leng Tan (see the acknowledgements in the catalogue), Ray’s associate, is not well-versed in mathematics.
5. The broad mathematical discussion in general at the end is vague and imprecise.
6. A reference to a book by the authority Asian architecture expert George Michell, which at first sight leads to this particular jali, is misleading. I obtained the book, but this jali was not there. Rather, the reference was generic to jalis and not specific, as hoped for.

References
¹ George Michell. The Majesty of Mughal Decoration. The Art and Architecture of Islamic India, 2007, pp. 69–70.

(b) Simon Ray - Islamic and Indian Art Dealer
Ray is one of London's leading fine art and Islamic and Indian Art dealers, and so weight should indeed be put upon this entry as to veracity in all senses. However, it is also well to reexamine. I begin by examining the date. From the sparse detail to hand, the 17th century gives us from 1601–1700, whilst the Mughal era was of 1526–1540 and 1555–1857, the latter of which offers no extra clue. Therefore, the date is given within a hundred years. It is not clear how the date is attributed. Is this knowledge of his field or documentation? Early jali work was built by carving into stone, generally in geometric patterns, while later the Mughals used very finely carved plant-based designs, as at the Taj Mahal. Possibly the date is based on this. Another clue is possibly afforded by the colour of the sandstone, yellow. Red sandstone in general appears the more popular. However, I have been unable to establish if there is any significance as to periods here. Interestingly, and curiously, the other entries are much more detailed, which suggests that there is little more known than what is already given. Jalis, in all forms, of history, and its intricacies, are not my field, although I have of course read up on this a little, and so I bow to Ray’s greater knowledge here. As such, from reading up on Ray’s interest in Islamic Art, of which he is an authority, and given that he is head of such a noteworthy company, I will accept the date given as true, albeit with due reservation. Of interest is that this is the only known jali of the Mughal period with a Cairo tiling. No mention is made of the Cairo tiling on the pages, unsurprisingly, and so whether the Cairo tiling is known to Ray is unknown. However, without any obvious mathematical background or interest, it is unlikely that Ray would be familiar with this association. So far as I am aware, this is the only appearance of this jali in print. More modern-day Cairo tiling jalis (21st century) can occasionally be seen.

(c) Enquiring with Simon Ray on the Jali
Of some not inconsiderable interest is the age and provenance of the jali. Although 17th-century is given, this is not documented, and notably, and regrettably, the provenance is not stated. Naturally, on account of the great age here, of which if so is the earliest extant instance of a Cairo tiling by far, of no less than three to four hundred years, predating that next confirmed reference of the early 1900s (not a jali), and so is thus historically an artefact of the utmost significance. Therefore, I attempted to contact Ray to find more details on this. However, despite his email address being freely available (and so appearing to welcome queries), this was to no avail. Despite an obvious bona fide query in his field, two emails went unanswered. As detailed above, given the historical aspect, I was loathed to give up on this, and then at my behest two others from interested parties of the Cairo tiling from academia also wrote to him, namely professors Gregg De Young (American University in Cairo) and Chaim Goodman-Strauss (University of Arkansas), stressing their academic credentials, but they still met with no reply! In the midst of this, I then tried other ways. I also contacted his associate, Leng Tan, who wrote the captions, but he too did not respond. Another was George Michell, of whom the book he quotes in the references, but who also did not reply (although, as he was not directly involved with this jali, I do not unduly castigate him here, in contrast to others). I also phoned Ray’s office, and although Ray was unavailable, I spoke to one of his assistants who reliably informed me that the details in the catalogue would be true. However, without any provenance, this remains far from satisfactorily resolving matters. It is infuriating! Even if not of a detailed reply, just a few words as to provenance would surely not be asking too much of a genuine enquiry in their field? Perhaps we all are simply too small fry to bother with; from what I can make out, his company turns over millions of pounds a year. But for whatever reason, Ray and his associates choose not to answer. Come on, Simon, in the unlikely event of your reading this, redeem yourself here! All will be forgiven! Further, I also enquired with this as to the noted native authority El Nath, who, in addition to his website, has recently published (2018) a book on Mughal Jalis. However, he seemed to misunderstand my specific request, and so I did not pursue the matter. Ideally, I would have investigated the book, but as it is a little expensive, and from seeing what is likely the material on his website, placed in a book, I decided not to pursue it.

PART 2  - Jali Analysis - Inner and Outer Parts

(a) Jali - The Two Tilings
The jali is interesting in itself as a ‘jali within a jali’, of in effect another, different tiling. So far as I can establish, this is the only instance known (I here disregard some ‘mini-subsection’ instances, divided into rectangles). However, despite the jali seemingly consisting at first sight of two unrelated tilings, of pentagons and octagons, these can be seen to be related, as first pointed out in correspondence in January 2019 by the geometer George Baloglou. In short, it is possible to overlay a Cairo tiling onto suitable octagon tile vertices (Fig. 2). Furthermore, it can be seen that the subsidiary hexagons from any one tiling match the other. Therefore, each tiling can be transposed from one to the other. Aesthetically, this is most pleasing indeed, and reflects well on the (unfortunately anonymous) designer! This can hardly have been accidental; it must have been purposeful. Indeed, he has gone up even further in my estimation!

(b) In Situ Angle Analysis or The Determination, in principle at least, of the pentagon angles

Of obvious interest is the determination of the angles of the pentagons, of which this is perhaps, not unsurprisingly, unaddressed in the Ray catalogue. However, as I discuss below, the matter is not easily resolvable for a variety of reasons. First, I am unable to measure the angles in situ. Second, of necessity, I have to rely on an image, which is, on the face of it, not ideal, in that in such circumstances the picture is typically shown at an angle, which is hopeless for determining such exact and demanding angle matters. However, the matter is aided in that one of the pictures I have to hand is just about as ideal as it will get, face on, without any perceivable distortion! However, measuring the angles is still not as easy as it may otherwise appear to be! There are problems in outlining the defining pentagon. A problem arises in defining the vertices due to the nature of the jali, of chiselled, grooved lines, along with the inadvertent minor imperfections of the artisan. Defining an exact spot to place a vertex is difficult. For instance, see the second pentagon, lower. This is noticeably distorted by the carver. However, there are indeed ‘indications’, where lines cross and meet, and in my assessment, it is possible to be accurate to a reasonable assessment, but not to the nearest degree with any amount of confidence, at least of a single arbitrary measure. One drawback is that the image is relatively small and so susceptible to error measurement. In short, to measure this by hand with a traditional protractor is problematic; it is far too crude a means. By far the best solution is to import the image into a dynamic geometry software, such as GeoGebra (my favoured software), which will permit enlargement (albeit here with the loss of resolution). When so enlarged, great accuracy can be assumed. Further interactive adjustment is possible, if so desired, and so measurement with much greater accuracy than by hand is possible. Note that the following figures should be borne with the above in mind; true right angles were not always possible. The slightest alteration of a vertex can result in movements of many degrees. To this end, I outlined ten pentagons, which I judged a sufficient number to sample to give a broad indication, and measured the angles directly on the jali, and listed them as tables, below, Fig. 3.

Data as a table, Top, rounded up and down to the nearest degree 

Average: 114, 134.2, 112.8

To say the least, there are considerable vagaries here, of the two variable angles, much more so than I was expecting. Even when the 90° angle is known, this does not always show as 90°. For any one set of data, to determine the angles here, to a degree, is simply impossible; only a rough indication is possible. However, when the above angles are averaged to the nearest degree (mean, excluding the known 90°), this gives a typical pentagon of (top section) 111.4, 137.2, 112.4 and (lower section) 114, 134.2, 112.8. An immediate observation is that this is very close to the aesthetic and special ‘Cordovan Pentagon’, so named and popularised by Redondo and Reyes, following in the footsteps of the Spanish architect la Hoz, of the variable angles of 112.5° and 135°. Fig. 4(a). However, with such vagaries, this is not necessarily convincing. A distinct possibility, yes, but not definite.  What is needed is a more compelling measure. A convenient feature of this particular pentagon is that when it has a side extended, it can be seen to alight on a vertex (Fig. 4(b), which is a rare feature of a generic Cairo tiling (there is one other possibility).

Fig. 4. Cordovan Pentagon. (a) with angles, (b) with angles and side length extended, alighting on a vertex

 Jali - In Situ Analysis by Extending a Side Length
To this end, I now suitably extend the side of the jali. As can be seen,  within the limitations of the image, it alights on a vertex (Fig. 5). Again, I use more than one instance; five, as a 'fair sample'.

From this, it would indeed appear to alight on a vertex, and so a reasonable supposition is that this is indeed a Cordovan Pentagon! If it is indeed the Cordovan pentagon, it would be very pleasing, and of this opens up further questions as to why this specific Cairo pentagon, and not other pentagons. As I show on my ‘Minima to Maxima’ page, there is a range of generic 'incremental angle' Cairo tilings, from minima with a rectangle, to maxima with a square. However, only a few can be seen to have special properties, as likely exemplified by the above instance. Further, it can be seen to be exactly mid-range of the 91 pentagons in that listing, and so it can be described as the most average of all. Below, I show a condensed listing from that page, showing the mid-range aspect.

INSERT TABLE

(c) The Construction

Therefore, all the indications are that the pentagon was specially chosen/devised, as against a generic instance. However, this is not necessarily so! As I show below, the  Cordovan tiling is easily drawn by one of two methods, involving octagons. I now believe that the tiling thus arose by default, without any considerations as to the alighting feature. In short, this feature is a 'happy accident'. However, the question then arises as to how this was drawn. Such specific angles of a single pentagon and then suitably repeated three times to form a unit hexagonal repeating cell are not readily drawn by the tools of the day, or indeed even now by a traditional compass. However, as alluded to by the Cordovan proportion, with its underlying octagon premise, this can be seen in the pentagon here. More than likely, it was devised by a regular octagon, in one of two ways: Fig. 6(a) by a semiregular tiling 4.8.8. (square and regular octagon tiling) or Fig. 6(b) overlapping octagons suitably arranged. Whatever the method, both require an additional intervention for the baseline. Both methods are relatively simple, and one of these I consider must have been used. However, I consider the overlapping octagons by far the more obvious choice, on the grounds of simplicity.

Interestingly, to give further support to my hypothesis, octagons can be seen to be used in other jalis, as I discuss in depth separately. Further, Emil Makovicky and N. M Makovicky in a paper discuss octagons in Mughal jalis, as does E. H. Hankin. Further, overlapping octagons can be seen at the Taj Mahal. Admittedly, all this is unrelated to the pentagon here, but this shows that octagons were very much in the mind of Mughal designers, and so is a more than plausible construction than this one-off instance of mine shows.

Despite much progress, open questions abound:

1. How did, and by what means, did it get to London? This is a substantial heavy artefact, probably weighing hundreds of pounds! 

2. What has become of the jali? Presumably, it has been sold, as it does not appear in later years of his catalogue, up to and including the present day (2019; the 2020 catalogue has yet to be made available). I have not seen any other references to this jali elsewhere.

3. The designer. Were there many jali designers, or just a few? Are any names known? Was there a ‘pattern book’ of the day?

4. Does the pentagon design (and the designs in general of jails) have a name?

Conclusion

As such, I consider the finding here of a precursor to the (presumed) Cordovan pentagon, highly significant, if indeed this is so as determined by my analysis above, as well as the presumed accuracy of the dating of the jali by Ray. This is the first Cairo-like tiling known, by no less than three-four hundred years! The designer must surely have been aware of at least some of its special attributes. Therefore, in his honour, in recognition of his heritage, I am now proposing to call this the ‘Mughal Pentagon’.

References

Abbas, Masooma. ‘Ornamental Jālīs of the Mughals and Their Precursors’. International Journal of Humanities and Social Science Vol. 6, No. 3; March 2016. 

http://www.ijhssnet.com/journals/Vol_6_No_3_March_2016/16.pdf

A good general guide to jalis.

Bailey, David. ‘Minima to Maxima’. (Webpage)

http://www.tess-elation.co.uk/cairo-tiling/minima-to-maxima

A listing of all possible pentagons, in ½° incremental angles, where the tiling degenerates to a square and rectangle (the latter in a basketweave configuration).

Gil-López, Tomás. 'The Vault of the Chapel of the Presentation in Burgos Cathedral: “Divine Canon? No, Cordovan Proportion”', April 2012, Nexus Network Journal 14(1)

https://www.researchgate.net/publication/257314781_The_Vault_of_the_Chapel_of_the_Presentation_in_Burgos_Cathedral_Divine_Canon_No_Cordovan_Proportion/link/580c637608aeef1bfeeb62c0/download

Of general Cordoba interest, but is notably without any pentagon discussion.

Huylebrouck, Dirk, A. Redondo, and E. Reyes. ‘Octagonal Geometry of the Cimborio in Burgos Cathedral’. Nexus Network Journal 13, 2011, pp. 195–203.

https://www.researchgate.net/publication/225784187_Octagonal_Geometry_of_the_Cimborio_in_Burgos_Cathedral

Of general Cordoba interest, but is notably without any pentagon discussion.

Hoz Arderius, R. La proporción Cordobesa. Actas de la quinta asamblea de instituciones de Cultura de las Diputaciones. Ed. Diputación de Córdoba, 1973. NOT SEEN

Translated: The Cordovan proportion. Minutes of the fifth assembly of Culture institutions of the Provincial Councils.

Hoz Arderius R. Rafael de la Hoz. Consejo Superior de los Colegios de Arquitectos de España. Córdoba (Spain) (2005). NOT SEEN

Translated: Superior Council of the Colleges of Architects of Spain.

Makovicky, E. and N. M. Makovicky. ‘Nonperiodic Octagonal Patterns from a Jali Screen in the Mausoleum of Muhammad Ghaus in Gwalior and Their Periodic Relatives’. Nexus Network Journal 19(1):1–20 November 2016.

https://www.academia.edu/36894338/Nonperiodic_Octagonal_Patterns_from_a_Jali_Screen_in_the_Mausoleum_of_Muhammad_Ghaus_in_Gwalior_and_Their_Periodic_Relatives

A general discussion on octagons in Mughal jalis; the possible connection to my hypothesis is not addressed.

Michell, George. The Majesty of Mughal Decoration. The Art and Architecture of Islamic India. Thames & Hudson, 2007.

Quoted in Ray’s Islamic catalogue of 2016. 

Nath, R. Mughal Jali Art: Perforated Stone Screens & Railings in Mughal Architecture. The Heritage Ajmer/Jaipur/ INDIA. First edition 2018. NOT SEEN

Ray, Simon. Indian & Islamic Works of Art. Self-Published Catalogue, 2016, pp. 178–179.

https://www.simonray.com/catalogue_2016.htm

(The entire catalogue)

Redondo, A. and E. Reyes (2008a). ‘The Cordovan Proportion: Geometry, Art and Paper folding’. In: Proceedings of 7th Interdisciplinary Conference ISAMA 2008-Valencia, Spain. Hyperseeing, May-June, 20008, pp. 107–114.

‘Cordovan pentagon’, i.e. a Cairo tiling, is given here for the first time. The same research is repeated, with seemingly minor variations, in three other publications by the authors. 

Redondo, A. and E. Reyes. ‘The Geometry of the Cordovan Polygons’, Visual Mathematics, 10, No. 4, 2008.

www.mi.sanu.ac.yu/vismath/redondo2009/cordovan.pdf

Redondo, A. and E. Reyes. ‘Cordovan Geometrical Patterns and designs’. Symmetry: Art and Science, 009/1-4. Special Issue for the Conference of ISIS-Symmetry. Symmetry of Forms and Structures, Wroclaw-Cracow, Poland, 2009, pp. 68–71.

Redondo, A. and E. Reyes. ‘Geometry and Art from the Cordovan Proportion’. In ‘Mathematics and modern art’. Proceedings of the first ESMA (European Society for Mathematics and the Arts) conference, Paris, France, July 19–22, 2010.

https://www.researchgate.net/publication/268271057_Geometry_and_Art_from_the_Cordovan_Proportion

Reyes, Encarnación and Inmaculada Fernández. Pentágonos. Construcciones. Mosaicos, Geometría sagrada. (in Spanish). Universidad de Valladolid, 2015.

Translated: Pentagons. Buildings. Mosaics, Sacred Geometry.

See p. 156.

Varanashi, Satyaprakash. ‘The multi-functional jaali’. The Hindu. January 30, 2011.

https://www.thehindu.com/todays-paper/tp-features/tp-propertyplus/The-multi-functional-jaali/article15538427.ece

Of general interest, on the decline of jalis in modern-day India.

19 June 2025. Updated from Google Sites Conversion. The conversion had left the page in disarray, unable to accommodate tables, resulting in a poor, at times, disjointed presentation. This I now improve. The text has also been corrected in Grammarly (with more corrections than I would like to admit), pending a more extensive analysis after the initial overhaul. Also, I have removed Part 3 text, as this was not strictly on the 17th-century jali, although still relevant. As the page was already quite lengthy, I considered this distracted from the main text, hence its removal (available at Wayback Machine).

Page Created 10 August 2020. Continued ad hoc 11–14, 17–20, 24–28 August as 'Release 1', of 28 August 2020.