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Introduction and Background
In various books and articles on tessellation, a reference to a pentagonal tiling known as the ‘Cairo Tiling’ (or similar, such as ‘Cairo pentagon/tessellation//paving’) is commonly to be found (with descriptions such as ‘frequently seen’ and ‘many of the streets are paved…’), said to be found in Cairo, Egypt, hence the title. However, amazingly, although often discussed in the literature and illustrated with a line drawing, this is not shown in its most obvious incarnation, as portrayed on the streets of Cairo. Until recent times, despite extensive searching, I have not been able to find an in situ picture of this. Note that here I emphasise ‘picture’, contrasting this against a line drawing, which is invariably found in all quoted sources. Indeed, I believed that this might at one time be just a ‘mathematical urban myth’, given that I had found no pictures, or had no referenced first-hand sources until recent times. Indeed, I was aware of this ‘no picture’ situation from as far back as 1987, from which date I examined various likely books and articles for this without any success, albeit largely ad hoc. However, upon my recent research in this (2010), I took a more proactive and thorough approach than previously, in different ways and means. This involved a plea on the website for an in situ ‘Cairo tiling’ picture. In conjunction with this, I also entered into personal correspondence with ‘likely people’ (mathematicians) who may know something of this (John Sharp and Brian Wichmann, who looked in their libraries). Also, postings were made on the academic forums (Tiling list server) and an Islamic tiling site (Archnet). However, all this was to no avail; all of which bore no immediate fruit. However, subsequently, the website request finally paid dividends. Helen Donnelly, an artist from the UK visiting Cairo (November 2010), who, with her artist’s eye and interest piqued when she saw it on the streets, researched it on the web, noticed my request and reported it back to me, followed by a succession of pictures of it in different places. The ‘additional’ sightings were quite a surprise; given the lack of previous pictures, I thought the tiling must be incredibly rare, perhaps only appearing once, maybe twice, perhaps not even after all, as alluded to above, or perhaps had subsequently disappeared, i.e. been replaced. But on the contrary, it isn’t in short supply; unbelievably, it’s quite common, all over Cairo, and further afield! Additional sightings by Donnelly were made in other locations in quick succession, not once, twice, but many others; in total, nine sightings over four Cairo districts (Dokki, El Behoos, Mohandiseen, and Giza). Incredibly, on one occasion, there were two sightings in a single day! Furthermore, and most unexpectedly, the pictures did not essentially simply repeat themselves as may have been thought. The tiles come in two distinct forms: in a square matrix, with the pentagons inscribed, and as single pentagons, with a curious ‘many-polygon’ texture. Also, the tiles themselves were clearly of different periods (with obviously new tiles, being pristine, and old, with considerable wear), along with innovations regarding colouring. Upon Donnelly’s departure in December 2010, of which the story might at first glance be thought complete, it unexpectedly took off again in September 2011, with continued investigations. Upon asking an ex native Cairo mathematician, Mohammed Yousif, he put me in contact with Gregg De Young of the American University in Cairo (AUC), who told me the paving was used extensively at the AUC, and also much further away (450 miles), at the Old Cataract hotel, in Aswan (regrettably, no longer extant; it was removed and replaced during a 2008 renovation). Upon even further investigations of September 2011, with Pam Garnett of the El Alsson school in Cairo, further pictures arose from different locations outside of Cairo, with sightings in Alexandria (outside the Roman amphitheatre), El Alamein (War Museum), and St Paul’s Monastery grounds. Subsequently, other places were found upon continued web and book searching, at Heliopolis and Al-Azhar University.
All the pictures are quite astounding in their sheer frequency and extent of the tiling, in which it can be described as ‘spectacular’, frequently covering many hundreds of square yards in courtyards and whole street lengths. And this is not to mention less spectacular occurrences, in that after this page and subpages (in which I report its findings and show in situ pictures), the fact that there are ‘no pictures’ makes this all the more surprising (or at least purposefully so)! However, ‘no pictures’ should be qualified, as this is not to say that the tiling has not appeared in print and on the web, as it indeed has, but with only what I term as ‘incidentally’. As far as I am aware, it has never been shown purposely, in that the subject matter of the picture is something else. Only nine instances are to be found, and only four of these are unambiguous, as detailed on the 'Sightings in Books' page. Likely, there are other travel guide books where this has occurred (and I would be indebted to any reader who can draw my attention to others).
Also, instances online can be found in blogs and picture databases (for example, at the El Alamein War Museum grounds). But again, all instances are incidental, in that the paving appears not purposeful. Occasionally, the paving is indeed found in a sense ‘purposefully’, in that the photographer has found the paving ‘interesting’ enough to photograph as an entity (Pam Garnett and Craig Scott, who posted pictures on a blog and picture site respectively), but were unfamiliar with the significance of the ‘Cairo tiling’ description. In contrast, the pictures here are the first, or so I believe, associated as the ‘Cairo tiling’.
In the course of my investigations, the study has expanded considerably from the initial search of a single, in situ picture. This primarily takes the form of the various sightings, mathematics of the tiling, and history, loosely stated. Indeed, it has enlarged so much that the material cannot be accommodated with ease on a single page. Consequently, ‘additional aspects’ are shown as subpages:
Acknowledgements – Listing my various correspondents, and their contributions to the investigation
Aesthetic Cairos – With a framework of what is recognised as a ‘Cairo tiling’, some instances that rise above others due to their aesthetics, typically with lines of collinearity
As Architecture – Instances of the Cairo tiling in architecture, worldwide in Australia, Belgium, Croatia, Japan, United Kingdom and United States
As Flooring – Instances of the Cairo tiling as flooring, worldwide
As Wall Coverings – Instances of the Cairo tiling as flooring, worldwide
Collinearity – An analysis of the premise of collinearity
Colouration – Analysis of different ways of colouring the tiles per se, and as found in the in situ pavings
Defining a Cairo-type Tiling – What exactly ‘is’ a Cairo-type tiling
First Photographs – The earliest extant pictures, ‘late 1960s’, from (and at) the American University in Cairo
Foreign Cairos – Instances of the paving outside of Cairo, of other countries, all likely independent of Cairo, in Japan (street paving at Hamamatsu and Tokyo), and Germany (as a flooring, at Hamburg Music Hall, likely of c. 1904)
Link to Type 13 Convex Pentagon – An observation of mine as to the connection between the Cairo tiling to the type 13 convex pentagon, likely used by Marjorie Rice to make her discovery
Martin Gardner Mystery Resolved – Gardner reports a ‘Cairo tiling’ in ‘Mosaics of Moorish buildings’, but this is a false sighting.
Miscellany - Attraction – The tiling has been much discussed and praised for its aesthetics, but just what is it that attracts so much florid prose? I examine various authors' comments; Manufacturer – Speculations concerning the manufacturer, which remains unresolved; Furniture - Modern day usages; Flooring – A curious instance as a flooring (in contrast to pavings), in a downtown Cairo apartment block, the only such instance found so far, possibly as early as 1950s
Pentagon Confusion – An analysis as to why the pentagon is so frequently incorrectly described as equilateral or the dual
Personal Account – The story of my interaction with Helen Donnelly, focusing on the thrill of discovery, and subsequent chase, rather than with any mathematical elements
Pictures of Sightings 1 – A general collection of the various places and forms the paving takes in Cairo
Pictures of Sightings 2 – a general collection of the various places and forms the paving takes outside Cairo (but still in Egypt)
References – Listing instances in books and articles where the association with Cairo is made (i.e. the Cairo tiling is frequently…)
Requests/Questions – Despite much progress made, some aspects remain unsolved. This asks some unanswered questions I have
Sightings in Books - All occurrences of the paving in books
Six Fallacies - widely repeated incorrect claims
Study 1 – A study of the mathematics of various ways of composing a Cairo tiling, here within a square matrix that is reflected
Study 2 – A study of the mathematics, as above, but here with a rectangle
Videos – Instances of the paving captured on video, at the AUC; this allows one to see the sheer extent much better than a photograph
However, despite excellent progress being made, in that I now have pictures to hand, and from numerous different locations, many important questions, mostly of a historical nature, still remain:
1. How old is the tiling? The oldest report I have is of 1956 (at the Al-Galaa club, Heliopolis). Can anyone antedate this?
2. Who or what body was responsible for installation of the tiling? I now (June 2016) have found the designer, a Ramzi Omar! More detail to follow
3. Is the tiling still being manufactured, and if so where? For certain, it was originally manufactured by the Nile tile company, albeit not now. Quite when they ceased producing it is unclear. Does anyone know? Likely it was then licensed out after a while. I have tentative reports of it being made in Basateen, and anecdotal reports at Aswan, and possibly Heliopolis, but without any detail whatsoever. Detail is sought.
4. Where else is the tiling to be found in Cairo, and in other parts of Egypt? I have sightings in Cairo (in order of discovery) at Dokki, El Behoos, Mohandiseen, Giza, Maadi, Heliopolis (Al-Gaala Club, Caesar’s Place hotel), American University in Cairo (downtown, the university has recently largely moved to new premises), Gezira (Sporting Club), and Al-Alzar (university). I’d like to know of others. Other parts of Egypt it is seen in include Aswan (the Old Cataract Hotel), Alexandria (amphitheatre), and El Alamein (War Museum grounds). I’d like to know of others.
5. Has the tiling appeared in print previously, either incidentally or purposefully? Likely, given its prevalence, it has indeed appeared, but despite this, aside from the eight instances listed above, nothing. Likely it would appear incidentally in newspapers, but searching these is impractical. I’d like to know of others.
Requests:
1. Would any reader of this web page know of any additional pictures and references to the Cairo tiling in books and articles other than those here on the references page? I would indeed like to see additional pictures and references, the earlier the better.
2. Historical pictures are sought of the sightings in Aswan (the Old Cataract Hotel), now no longer extant, and El Alamein (War Museum). The earliest confirmed dates are 1998 and 1994, respectively. Likely, both are much earlier, perhaps by many decades, but exactly how early is unclear. I’d like to know about antecedents.
3. If any reader of this web page is intending to visit Cairo, or knows of someone who is intending to do so, or has contacts in Cairo and who would be interested in joining/aiding in the investigation, they would be warmly welcomed. In particular, is there anyone willing to visit the patent office to view the (likely) patent? Also, any new sightings in other locations would be warmly welcomed. Email me with any further details.
4. A Plea for an Arabic Speaker and Investigator. Although much has been achieved with the investigation, there are still some aspects left unresolved, some, but not all, caused by my (and my English-speaking investigators') lack of Arabic language ability. In particular, one outstanding issue is that of finding the patent which surely exists (it is mentioned in an advert, seemingly registered under the name of the Nile Tile Company owned by Ibrahim Abdel Hafez, under number 451), and which will presumably show the exact geometry, which is unclear. From the pictures alone, it is not possible to be sure of this. Is there any reader here (or know of another person) who is fluent in Arabic and is prepared to visit the Egyptian Patent office in Cairo, at Kasr El Aini Street? If need be, I am more than willing to pay someone here. Just name your price! Even if the outcome is negative, i.e. there is no patent, I can at least rest assured and move on. You will still be paid! Or, determine the matter on their website. If it’s there, I cannot find it!
18 June 2025. Updated from Classic Sites. A general overhaul of the text in Grammarly, pending reappraisal of the page. Minor changes in text placement were also undertaken.
Created: 25 November, 2009, with many revisions too numerous to list! Recent update: 22 June 2013, 'Sightings in Books' page. 20 October 2015. A general updating of findings since the last recorded update of 2013
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