In various books and articles on tessellation, a reference to a tile known as the ‘Cairo Pentagon’ is commonly to be found, supposedly a paving based upon an equilateral pentagon, said to be found in Cairo, Egypt. However, despite extensive searching, I have not been able to find a picture of this. Note that here I emphasize picture, contrasting this against a line drawing, which is commonly to be found. Therefore, is this just an mathematical urban myth? The earliest reference I have to this is Martin Gardner’s Mathematical Games article in Scientific American of July 1975, where in conjunction with an article on tiling the plane with convex polygon tiles, and more specifically on the different types of pentagon, he mentions a ‘Cairo Pentagon’ tiling. Admittedly, although these words do not appear in combination, the implication is that there is such an entity as a ‘Cairo Pentagon’. He states, page 114, concerning a line drawing of a tiling of equilateral tessellating pentagons, Figure C, page 116 (the brackets are my own):

He also gives a construction on page 117. However, despite many years of searching for a picture of this in situ, I have yet to see this as described. Other authorities also allude to this, but show no picture:

Doris Schattschneider in the article 'Tiling the Plane with Congruent Pentagons', in Mathematics Magazine January 1978 states, page 30:

 It is said to appear as a street paving in Cairo.

This is interesting, as she qualifies this statement  by 'It is said', probably referring to Gardner's article. However, this pentagon, her Figure 1, is not a equilateral pentagon. 

Robert Fathauer’s new (2008) book Designing and Drawing Tessellations, has a brief discussion on tessellations in the 'real world', page 2, with many photos of brickwork and paving stone tessellations, all except for the ‘Cairo Pentagon’ tiling, where although this is discussed he shows a line drawing. Presumably, he was unable to locate a photo of this. Other books are similarly of the same shortcoming. 

On the web, Wolfram MathWorld and Wikipedia simply give a line drawing. A Google picture search reveals nothing. 

Although admittedly I have not got or seen every book on Islamic-type tilings, I have most of the popular ones, any one of which would surely have shown a picture of this in situ  if readily available. However, none do. Therefore, is this an mathematical urban myth or not? Can anyone locate a picture of a ‘Cairo Pentagon’ tiling in situ?

Upon searching the web lately, I see another site, by Mark Thompson has found the same situation and is posing the same question http://home.flash.net/~markthom/index.html. I've tried contacting the given email address, but it bounces. Has anyone got a current email? 

Last Updated: 25 November, 2009