Cairo Tiling

Stop Press 20 March 2017.
Upon continued investigations, the first picture of the designer of the Cairo tiling, Ramzy Omar!  However, as yet, there are none of Ramzy with the tiling. Ramzy was a notable architect of the day, and a confidant of President Nasser and President Sadat, all which only adds to the story, with the great man pictured here with President Sadat. Indeed, in the greater scheme of things, probably the Cairo tiling was one of his lesser accomplishments, with 22 major architectural projects in Cairo and elsewhere to his name, such as the Sheraton Hotel, and he was also the designer of the Egyptian flag!  A website on Ramzy and his many accomplishments has recently been put online, of which this contains much background details of his life story, although as such the Cairo tiling is not mentioned:
More detail to follow.

© Tarek Fikry

The first purposefully published in situ pictures of the two types of Cairo pentagon tiling?
© Helen Donnelly
Figure 1, Cairo, Outside Behoos Metro Station, Figure 2


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 emphasize ‘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 be 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, of which from such a date I examined various likely books and articles for this without any success, albeit largely on an ad hoc basis. However, upon my recent researches 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 site 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 was 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 wearing), along with innovations as regards colouring. Upon Donnelly’s departure in December 2010, of which the story might at first glance be thought complete, it unexpectedly took of again in September 2011, with continued investigations by me. 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 the 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 subsequent to this page and sub pages (in which I report its finding 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 purposefully so. 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 so that the material cannot be accommodated with ease on a single page. Consequently, ‘additional aspects’ are shown as sub pages:

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

Architecture – Instances of the Cairo tiling in architecture, in Belguim, Croatia, Japan, United Kingdom and Australia

Bisymmetric Hendecahedron – A apparent polyhedral relation

Collinearity – An analysis of the premise of collinearity

Colouration – Analysis of different ways of colouring the tiles per se, and as found of 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 as 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

Notable Sightings – American University in Cairo – Some of the sightings are more notable than others, for various reasons. Some are associated with a major institution, such as the AUC and so has potential for being dated

Notable Sightings El Alamein War Museum – A sighting that has potential for being dated

Notable Sightings Old Cataract Hotel – A sighting that has potential for being dated; the Old Cataract being one of the ‘Grand Hotels’ of Egypt

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, focussing on the thrill of discovery, and subsequent chase, rather than with any mathematical elements
Pictures of Sightings – 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 being made, some aspects remain unsolved. This asks some unanswered questions I have

Sightings in Books -  All occurences 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? 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.


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 sighting in
Aswan (the Old Cataract Hotel), and El Alamein (War Museum). The earliest confirmed dates are 1998 and 1994 respectively. Likely, both these are much earlier, perhaps many decades, but exactly how early is unclear. I’d like to know of antecedents.

3. If any reader of this web page is intending to visit Cairo, or know 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. I am still searching for pictures at
Heliopolis and Gezira Island. Also; any new sightings in other locations would be warmly welcomed. Email me with any further details.

4. Can anyone identify this location in
Cairo, from a BBC interview during the recent 2011 unrest, in which an interview was conducted amidst a veritable sea of the paving. N.B. forward the video two minutes to get to the relevant tiling part:

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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