Hi, I’m David Bailey from Grimsby, England, with a keen interest in recreational mathematics, of a mostly geometrical nature, and more specifically of Escher-like tessellations along with their application to polyhedra. Additionally, I make the occasional foray into 'pure' tiling, such as pentagon tilings, and historical matters too, such as with the well-known 'Cairo tiling', 'cluster puzzles', 'houndstooth' tessellation and various Escher research. This website is thus dedicated to showing my own efforts in this field, along with some other aspects pertaining to the subject, such as various essays on tessellation, where I set my thoughts out, and are designed to be a tutorial in form.

The tessellations shown are most of what I term as of final, 'finished' examples, designed, drawn and coloured (generally of watercolour) by hand, and not a computer. These are essentially the product of a systematic study, which frequently belies various complexities that of necessity require a thorough approach. Also included are some that are best described as 'studies', of which, for various reasons, I have simply not found the time to complete as finished examples. These are thus simply denoted as ‘study’. Generally, but not always, the 'finished' and 'study' tessellations are accompanied by some explanatory text, whereby the various ‘intricacies’ behind the tessellation are discussed. In addition, each drawings colouration is discussed. The tessellations are so placed into distinct groupings as according to their motif, i.e. of birds, fishes ... as appropriate, with any further subdivision, due to there being so many examples of a specific motif (primarily of the bird examples) are thus put into arbitrary subcategories for the sake of general order.

Correspondence is welcomed: davidbailey500@googlemail.com

Follow me on Twitter! @tessellationfan

All images and text copyright David Bailey 11 September 2009


1. A Plea for an Arabic Speaker and Investigator

Although much has been achieved with the Cairo tiling investigation, there are still some aspects left unresolved, some, but not all, caused by my (and my English speaking investigators) lacking in 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 who is fluent in Arabic prepared to visit the Egypt Patent Office, at Kasr El Aini Street? Or perhaps interview Nadia Abdel Hafiz, his daughter, who now runs the company? If needs 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! That said, the patents seem to date only from 1970...


2. Password Access
Does anyone have access to: Project Muse, Shibboleth and OpenAccess log-ins and passwords? These are needed in conjunction with my studies. 

3. Journal Access
Does anyone have access to the following archives: Domus (an Italian journal), Mathematics Teaching magazine, 
Bloomberg Businessweek Magazine (a single article I want), and Vogue? Vogue is for my houndstooth investigations. Does anyone have any (institutional?) access? It costs a ridiculous $1575 (sic) for an individual!

4. Stanford University
Is anyone planning a visit to Stanford University? There is much in the Martin Gardner archive that I would like to see. But for a single request, in regards of my special interest in pentagonal tiling, I would very much like to see the contents of Box 33, Folders 8-12, and in particular papers by Marjorie Rice and R. B. Kershner. However, quite what the extent is here is unclear; possibly there is way too much material here to make ‘all’ available. In short, whatever you could make available to me, to whatever degree, I would be most grateful.
5. Escheriana
Does anyone have any Escheriana for sale, or of interest, or the Microfiches of all published work? Obviously, I am interested in seeing such matters.

Latest additions/revisions first. A complete list is on the 'update history' page. Minor (of a 'line or two') updates are ignored:


6 October. Cluster Puzzles, Themes - Noah's Ark

21 September. Cluster Puzzles, Generic Page - Rene Soriano

8-9 September. Cluster Puzzles, Themes - Countries & Continents

20 August. Cairo Tiling - 17th century Jali. A new page. Release 1

7 August. Cluster Puzzles, Themes, Nativity Scenes. A new page to the cluster puzzle page. Release 1 

29 July. Cluster puzzles, Dedicated Page - Angiolo Logi

17 July. Cluster Puzzles, Generic Page - Jerry Krider

16 July. My Library - By Subject Matter. A new page to the 'My Library' series. Largely for my convenience, rather than the reader.

14 July. Cairo Tiling -  Miscellaneous. Some Thoughts on Designing the Cairo Tile in Ancient History

30 June. Cairo Tiling - Minima to Maxima. A new page, with ad hoc additions into July and August. 

22 June. Cairo Tiling - Collinearity. An extensive rewrite of the page, in light of Daniel Piker's insight as to matters of the angles of the pentagon

1-5, 8-9 June (with further ad hoc minor returns). Cluster Puzzles - Götz-Peter Reichelt

26 May. Cluster Puzzles, Dedicated Page - George Luck

21 May. M. C. Escher - Research. Added 'Escher Spiral Themed Works - An Analysis'
20 May. Cluster Puzzles, 
Dedicated Page - Alex D. Palmer

7 May. Cluster Puzzles, Dedicated Page - Enzo Mari

30 April. Cluster Puzzles, Dedicated Page - M. C. Escher

14 April. Cluster Puzzles Dedicated Page- George J. Paulus. Release 1

8-9 April. Cluster Puzzles, Dedicated Page - Simplex. Release 1

2-3, 6 April. Cluster Puzzles, Dedicated Page - Elspeth Eagle-Clarke. Release 1

Since 16 January 2017