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

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? 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!


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

3. 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.
4. Escheriana
Does anyone have any Escheriana for sale, or of interest? Obviously, I am interested in such matters.

5. Vogue Archive
Does anyone have any (institutional?) access to the Vogue fashion archive (for my houndstooth investigations)? It costs a ridiculous $1575 (sic) for an individual!

Latest additions/revisions first. A complete list is on the 'update history' page. Minor updates are ignored:


18 July. Cairo Tiling - As Flooring. United Kingdom, Glasgow Physics Laboratory, text and image of quote added

17 July. Cairo Tiling - As Paving (Exterior to Cairo) and Architecture. Croatia, Rijeka. A major reappraisal of Zamet Centre, with text expanded and with different pictures, to better show the dual-nature listing.

16 July. Cairo Tiling - As Paving (Exterior to Cairo) and Flooring. A major reappraisal of the Norway, Tromsø sighting, with text effectively wholly rewritten and expanded.

15 July. Cairo Tiling - As Paving (Exterior to Cairo). A major reappraisal of the Hørsholm, Denmark sighting, effectively wholly rewritten and expanded, with different pictures

12 July. Cairo Tiling - As Paving (Exterior to Cairo). Turkey sighting at an unknown location added.

11 July. Cairo Tiling - As Paving (Exterior to Cairo). A major reappraisal of the Switzerland, Basel sighting, effectively written for the first time.

10 July. Cairo Tiling - As Paving (Exterior to Cairo). A major reappraisal of the five Japan sightings. Text with minor retention, effectively wholly rewritten, with pictures.

9 July. Cairo Tiling - As Flooring. Women and Memory Forum, Cairo. Previously discussed as 'In Situ Oddments', without pictures. Text wholly rewritten, with pictures.

8 July. Cairo Tiling - As Flooring. 'German school'. Previously discussed as 'Foreign Cairos' with revised and slightly expanded text.

5 July. Cairo Tiling - As Flooring. Heidelberg Castle. Previously discussed as 'Foreign Cairos', without pictures. Text wholly rewritten, with pictures.

4 July. Cairo Tiling - As Flooring. Hamburg Musik Halle. Extensive revision from 'Foreign Cairos', of both text and pictures.

3 July. Cairo Tiling - As Flooring and As Wall Tiles. Daniel Ogassian added to both categories.

2 July. Cairo Tiling - Ramzy Omar. A dedicated page, on the designer of the Cairo tiling.

1 July. Cairo Tiling - As Flooring. Szczecin, Poland, of a newly built (2014) philharmonic orchestra.

28 June. Cairo Tiling - Miscellaneous. Panelling (Bayer Pharmaceuticals, Buenos Aires, Argentina)

26 June. Pavement Tessellations. Kyrgyzstan pictures by Ian Claytor, text added.

24 June. M. C. Escher - Research. A new page, with my researches on Escher. The first is on his print 'Flatworms'. 21 June. Cairo Tiling - References. Update of the references page, with a non-attributed section references added, as well as as a general tidy-up.

24 May. Pavement Tessellations - Patents. A new sub page, of all aspects, including history.

9 May. Parquet Deformation. Douglas Blumeyer text and images added.

7 May. Where is... Thomas E. Foster relatives added.

6 May. Precursors to Escher. Hisui Sugiura text and image added.

25 April. Bowtie. A new page, on historical instances of the 'bowtie' tiling.

11 April. Cairo Tiling - As Architecture. The Ismaili Centre, London, text and additional image added.

15 March. Cairo Tiling - Architecture. Australia, Studio505 added.

12 March. Cairo Tiling - Architecture. One Smithfield building, Stoke, UK, text and imagery added.

6 March. Houndstooth. History page now considered 'polished' if not complete state, or at least not left obviously unfinished.

Since 16 January 2017