In various books and articles on tessellation, a reference to a pentagonal tiling known as the ‘Cairo Pentagon’ (or similar, such as ‘Cairo tessellation/tiling/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, despite extensive searching I have not until recent times 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 referenced first-hand sources. Indeed, I was aware of this situation from as far back as 1987, of which from such a date I examined various books and articles for this without any success. However, upon my recent researches in this (2010), in which I took a more proactive approach than previously, in which I asked on the website for an in situ ‘Cairo pentagon’ picture, as well as personal correspondence with ‘likely people’ (mathematicians) who may know something of this, and a posting on the academic tiling list serve, all of which bore no fruit, pictures have finally come to light, initially from Helen Donnelly, an artist from the UK visiting Cairo who, with her artist’s eye and interest piqued, researched it on the web, noticed my request and reported back to me with a succession of pictures. 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. But on the contrary, it isn’t; unbelievably it’s quite common! Additional sightings by Donnelly were made in other locations in quick succession, not once, twice, but many others; in total nine sightings over three Cairo districts (Dokki, 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, as the tiles themselves were clearly of different periods (with obviously new tiles, being pristine; and old, with considerable wearing), along with innovations as regards format, colouring and texture. Upon Donnelly’s departure, with continued investigations by me, further pictures from different locations arose, independently from Gregg De Young of the American University in Cairo (AUC) and Pam Garnett of the El Alsson school, who both currently reside in Cairo. 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, not to mention less spectacular occurrences, in that subsequent to this page (in which I report its finding and in show situ pictures), there are no pictures (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 elsewhere, as it indeed has, but with only what I term as ‘incidentally’, in that the subject matter of the picture is something else, the tiling appearing incidentally. Indeed, even this is infrequent, with only two instances, in travel guide books (in Egypt, by APA Publishing, where the subject matter is a mosque, and Fodor’s Exploring Egypt, where the subject matter is a hotel. Likely there are other travel guide books where this has occurred). Further, additional incidental sighting have also occurred occasionally on the web, e.g. where an international festival was organised; see the AUC Greek campus pictures. Although the tiles are prominently displayed, no reference is made to the tiling. Another incidental occurrence is where the photographer noticed the tiling had picturesque qualities per se (as has occurred with Pam Garnett, who posted pictures of interesting pavings in Cairo on her blog), but did not know of the Cairo tiling of the mathematical literature. Therefore, with all previous examples being of an incidental nature in all their various ways, to my way of thinking these do not count as bona fide sightings. Therefore, it is thus likely that these here are the first pictures in which the connection is clearly made, i.e. as a Cairo tiling.

The sub pages Cairo aspect is separated as according to distinct aspects of the theme:

§ Pictures from each district, accompanied by a discussion

§ An essay on what accounts for the ‘attractiveness’ of the tiling, in that although one of many tilings, very few are singled out as anything special in the aesthetic sense (as has occurred with the ‘Cairo tiling’ attribute)

§ A personal account, in which I relate the saga of my interaction with Helen Donnelly, focussing on the thrill of discovery, and subsequent chase, rather than with any mathematical elements

§ Various studies of the tiling per se, in which the mathematical aspect is explored, with variations of the theme

§ References, where I outline references to the tiling in books and articles

However, despite excellent progress being made, in that I now have pictures to hand, many important questions, mostly of a historical nature still remain:

1. How old is the tiling?

2. Who or what body was responsible for installation of the tiling?

3. Is the tiling still being manufactured, and if so where?

4. Is the tiling just restricted to Cairo, or is it found in other parts of Egypt? (I have a sighting and picture in Aswan, at the Old Cataract Hotel, 550 miles south of Cairo.)

5. What districts of Cairo is it found? I have sightings at Dokki, Mohandiseen, Giza, Maadi, and AUC at the Greek campus. I’d like to know of others.

Requests
Would any reader of this web page know of any additional references to the Cairo tiling in books and articles other than those here on the references page? I would indeed like to see additional references, the earlier the better. Also, if any reader of this web page is intending to visit Cairo, or know of someone who is intending to do so, any new sightings in other locations would be warmly welcomed. Email me with any further details.