Cairo Tiling

The first purposefully published in situ pictures of the two formats of the Cairo pentagon tiling, as seen on the streets of Cairo?

In various mathematical books and articles on tilings, a reference to a pentagonal tiling, with certain aesthetic properties, known as the 'Cairo Tiling' (or similar, such as 'Cairo pentagon/tessellation') 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 as a purposeful photo. A distinction should be made between the photographs. Although the paving is indeed previously pictured, this was by chance, appearing as background matter to whatever is being photographed, for instance appearing in travel guides.

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 just be a 'mathematical urban myth', given that I had found no pictures, or had no referenced first-hand sources until recent times.

In the general story, much fundamental detail is omitted. Specifically, this includes the date of instigation, the designer, and the geometry of the paving. Further, the paving comes in two forms, in a square matrix, with the pentagons inscribed, and as single pentagons, with a curious 'many polygon' texture, along with different colouring. This account thus reveals these aspects for the first time.

My own interest in the Cairo tiling began around 1986-1987, at the beginning of my mathematical interest in tilings, although exactly in which publication I first saw it I do not recall. From the beginning, I was impressed by the aesthetics of it. A surprising, although explainable feature, is the grouping of four pentagons into a parhexagon, overlapping at right angles. Although other tilings can be seen to possess overlapping features, typically the tile will be of a polygon lacking the simplicity of the Cairo pentagon. Undoubtedly, this feature helps to explain its popularity among mathematicians, with much fanfare, unlike other 'everyday' tilings.

The study is in (?) parts, namely that of the in situ pavings, the mathematics and variations and examples, undoubtedly independently, seen elsewhere, in other countries, in a variety of forms.

More details, with 34 subpages, including the Cairo tiling as jalis, architecture, flooring, paving, wall tiles, Ramzy Omar the originator, references, fallacies, and more, are at:
https://web.archive.org/web/20230412194454/https://www.tess-elation.co.uk

Part I The Cairo Tiling as Seen on the Streets of Cairo, Egypt

The paving/tiling is seen throughout the streets of Cairo, and indeed throughout all of Egypt, although not so widespread as the capital. There are many aspects to the discussion, including the first accounts, date of instigation, the designer, formats, and geometry, all of which I discuss.

1.1 First Accounts (Dunn, MacMillan, Gardner)

The paving was first described in the mathematical literature by James Dunn in 1971 [*], upon a visit to Cairo. It was then a little afterwards popularised by Martin Gardner, picking up on Dunn's account, in an article on tilings, in 1975 [*], Doris Schattsneider 1978 [*], and again by Robert H. Macmillan in 1979 [*], in an article with an Egypt theme and who also visited Cairo, and noticed the paving. Significantly, Macmillan pointed out (correctly) a feature of collinearity missing from the above. Largely from Gardner's exposure, this then led to a proliferation of expositions in articles and books. A curious feature is that an in situ photograph was not shown each time, but rather line drawings. And amazingly, this situation remained until this writing! See endnotes. An unfortunate feature of Dunn's account was an error in its geometry, stating that it is of an equilateral pentagon, but this is not so See endnotes. Following this, other incorrect statements were made, such as it was the dual of the 32. 4. 3. 4, Schattschneider 1978 [*]. In all subsequent accounts, the errors are repeated, with authors repeating the respective statements. Oddly, no author seems to have noticed the discrepancy., Unfathomably, Macmillan's correct account with a collinearity feature, something which is impossible with the equilateral and dual, was ignored! Of interest is the considerable length of time between its first appearance, in 1957, detailed below, and it attracting the attention of mathematicians.

1.2 The Manufacturer

The manufacturer of the paving is the Nile Co., the major paving company in Egypt, founded in 1942 by Ibrahim Abdel Hafiz (1942–2005), a pioneering Egyptian industrialist who personally ran the company's operations for over 60 years. However, despite contact with the company, much remains unknown about the instigation. Indeed, there is only one surviving document, an advert/flyer, announcing the company, instigation, designer, and other details that are associated with the paving! Given the widespread sightings, it must surely have been produced on an industrial scale and promotion, with accompanying adverts in newspapers, trade magazines and product information that would likely give more insight, but if so these have not materialised. Of interest would be to examine the company archives. However, quite simply, there does not appear to be much, if at all. It is not clear as to the extent, even if there are archives in the normal sense.

It is also not entirely clear that even today it is still being manufactured or is still available. A single paver has been seen in a Zamalek showroom, but whether this is just for show, or leftover, or is available for driveways etc. is unclear. The paving seems to have found a period of popularity before falling from use, but exactly when this occurred is difficult to say. Possibly this was down to the whims of the company, in that a change of design occurred after a while. Matters are complicated by the paving appearing in two formats, with single pentagons and in a square matrix, likely introduced at different times. The square matrix tiles do not appear in the early photos, with the first being seen in 1970.

1.3 The Advert

As alluded to above, there is but one sole document, an advert/flyer for the paving, from the Nile Co. Its importance cannot be overstated in the detail it contains; without it, fundamental details would otherwise have remained unresolved. Revealed is a stated designer, Ramzy Omar, the date of instigation, 1957, as well as other interesting details. It is not entirely clear if this is for a newspaper, brochure or flyer. But quite simply, whatever the outlet, it is indispensable! The different aspects of the ad are identified by numbers of my own addition. Each of these is outlined below, with the main points of interest then discussed in depth separately.

1. The date: 2 November 1957 - This has been added by the person who collected the advert
2. Company logo including stylization of the company name pronounced 'an-Neel' in Arabic
3. Nile Company for Supply of Architectural Materials
4. Ibrahim Abdel Hafez and his company
5. announce the introduction of their new product
6. in 7 colours (The large V shape is numeral 7)
7. Pentagonal paving tiles
8. For: The Borders of Swimming Pools, Gardens, Petrol Stations
9. Registered (as a patent) in the name of the company under number 451
10. Designed by the architectural engineer Amiralay Ramzy Omar (the title 'engineer' may be a purely honorary or symbolic title – it might not mean that he was a practising engineer.)
11. 21 Sixth Street (below the cement plant). The preposition here, like the preposition in English, has a variety of meanings and could mean either beneath or beyond or beside
12. T for telephone numbers 49851 – 79483 – 807604 – 803239

I now discuss each reference briefly in turn, followed by an expansion of the more important points.
(1) The date of instigation, 1957. This was previously unknown. The guideline photos were dated around the 1960s.
(2) Company logo including stylization of the company name pronounced 'an-Neel' in Arabic
(3) The company that manufactured the paving, The Nile Company. This was previously unknown. The Nile Company was (and still is) the foremost paving company of the day, and of which explains its widespread use throughout Cairo.
(4) The owner, Ibrahim Abdel Hafez. The owner was previously unknown.
(5) A new product. This clearly shows the tiling is not 'old' or 'ancient', as is sometimes given by others.
(6) The number of available colours, seven.
(7). Pentagonal paving tiles. Includes a picture
(8) Its purpose, of borders of swimming pools, gardens, and petrol stations. Curiously it is not stated as a general paving as such, although perhaps this would be too obvious to mention. Only one (historic) instance of a swimming pool sighting has been found, albeit with many private driveways, and none at petrol stations.
(9) Is registered as a patent, no 451. This document had not been traced. Likely this would reveal the geometry, although this can be surmised from the photos.
(10) The designer, Ramzy Omar. The designer was previously unknown.

Much is now established from this document. Of interest would be to examine the company archives. However, quite simply, there does not appear to be much, if at all. Searches of the company archives by * proved fruitless. It is not clear as to the extent, even if there are archives in the normal sense. Given the lack of historical pictures on their online outlets, such images may be few and far between. However, this may simply be down to the promotion of the business in an active sense, with historical matters judged of lesser interest. Who knows?

Unresolved Aspects of the Ad

Although from the above ad much can be gleaned, there are still aspects only partly revealed, with still unresolved aspects. The background of the designer, Ramzy Omar, can now be told. The ad mentions a patent, 451, which remains one of the outstanding unresolved matters. Likely this would give more detail. A search on the Egypt patent site proved unsuccessful. Possibly, the reason for this is that the patents on the site seemingly only date from relatively recently. Perhaps the earlier instances are awaiting digitisation?

1.3 The Designer - Ramzy Omar

The designer, as detailed in the advert, is Ramzy Omar (1916–2014) a notable architect of the day, and a confidant of President Nasser and President Sadat, all which only adds to the story, 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! Sadly, Ramzy passed away before I could make contact with him. What a missed opportunity. It could so easily have happened, with the investigation being in-depth from 2010, but I only found details of him in 2017, unfortunately a few years too late. Background matters of his work on the Cairo tiling are unfortunately not known; nothing more on his association has been found in the Nile Co. archives or family papers.

The only surviving document linking Ramzy to the Cairo tiling is the advert, in which he is clearly stated as the originator.

A full biography is at [*]

1.4 Historic Photos

Many instances of the paving can be seen in historical photos, although of course occurs by chance, with the paving appearing secondary to the subject matter. Many such photos are to be found in the President Nasser and President Sadat archives at the Bibliotheca Alexandrina library. Such photos show pictures from the very beginning, 1957, as well as widespread dispersal further afield in Egypt. Pleasingly, these are all dated, and to the exact day! Another good source is from the American University in Cairo archives, with photos of the Campus dating from the late 1960s, albeit the exact years are not always known. Research is also aided by pictures of prominent buildings. Photos also exist of the famed Old Cataract Hotel (the paving no longer extant). The first known sighting is at the Galaa club in Heliopolis, of 1957.

1.5. Spectacular Sightings

On occasion, what can be described as 'spectacular sightings' can be seen, with the paving stretching into the distance as far as the eye can see. Not all of these are now extant. These include:
Gezira Sporting Club, Gezira Island, of 1960s? (Extant)

The American University in Cairo (AUC) Downtown Campus near Tahrir Square (Semi-Extant)

The American University in Cairo See endnotes, sightings were some most extensive, and could be seen over most of the campus (of five city blocks), and noticeably the Greek Campus. However, most have now been replaced, with only a vestige of the paving at 'old' Greek Campus now remaining (it has recently been renamed GrEEk Campus). An open question is to the date of instigation. Quite when these were installed is uncertain. Certainly, they are 'old', as the first photograph (from the archives) of the AUC we have, of a date of a degree of certainty, is of 'late 1960s'.

1.6 Soap Froth Pattern of the Interior of the Individual Pavers

The individual pavers can be seen to have been divided into a mirror symmetrical 'many polygons' tiling, reminiscent, as Frank Morgan describes, of a 'soap froth pattern', of which term I will use to describe this feature.

Quite what the reason, if any, for this is is unclear. Generic pavings, worldwide, do not typically possess this feature. One possible explanation, as given by(?) is of a non-slip surface. However, it may simply be a decorative element without any other purpose. Curiously, there is a unique variant, in which the subdivisions, whilst retaining the mirror symmetry, are yet still finer. 

The paving is at the home of the AUC emeritus mathematician Michel Hébert, on his driveway on Aisha el Taymouriyya Street, Garden City. The 'soap froth pattern' can be seen to be notably different. By its very nature, this would suggest an 'early' instance (how early remains speculation), as it hardly seems likely that it would be introduced after, or amid, of the main production of the prevailing type (which is itself largely unclear). Speculating, could it have been a prototype of sorts, predating the other pattern? However, if so it can hardly have been a one-off. Likely, it must have been commercially produced, and so exists elsewhere, but if so I had simply not noticed it in my other sightings, being convinced (reasonably) that there was only one soap froth pattern. Upon investigation with Michel, he told me he moved into this building around 2000, and the paving was already in situ. From the condition of the paving, with some of the tiles having the pattern almost obliterated due to use, as well as general wear and tear, it is obviously 'old', but beyond a 2000 date, it remains speculation. Upon mentioning this to Gregg De Young, my collaborator in Cairo, he told me that a recent visitor of his, a historian of modern architecture, told him the building is from the 1950s or 1960s, and so plausibly the paving is too. Hébert's own investigations with the building's overseer also gives a more exact date of 1957, although there is no documentary evidence. Therefore, the exciting possibility arises that this is possibly the earliest extant sighting!

1.7 Format

Two formats are to be seen, of individual pentagons and pentagons (some truncated) inscribed in a square matrix. These measure 27-28cm* and 21-22cm*. However, on occasion both small and larger versions of the square matrix can be seen. On occasion some oversize square matrix can be seen

Created April 2024. Last Updated 6 May 2024