Navigation

Home

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, and historical matters too, such as with the well-known 'Cairo tiling', 'cluster puzzles' and the 'houndstooth' tessellation. 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 tutorial in form.

The tessellations shown are mostly 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.


At long last, the site was updated and rebuilt 11 September 2009, the first update since November 2005. Previously, the site was somewhat awkward to update (hence the hiatus), but with the advent of Google sites (which I wholeheartedly recommend), updating is now a breeze! So, look forward to much more to come, at regular intervals. 

Correspondence is welcomed: davidbailey500@googlemail.com

All images and text copyright David Bailey 11 September 2009
 
Request
Can anyone supply me with any of the following articles, which are needed in conjunction with my studies:

Pólya, G. "Über die Analogie der Kristallsymmetrie in der Ebene. Zeitschrift für Kristallographie 60 (1924): 278-282.

Niggli, P. "Die Flachensymmetrien homogener Diskontinuen." Zeitschrift für Kristallographie 60 (1924): 283-298.

Niggli, P. "Die topologische Strukturanalyse I." Zeitschrift für Kristallographie 65 (1927): 391-415.

Niggli, P. "Die topologische Strukturanalyse II." Zeitschrift für Kristallographie 68 (1928): 404-466.

Laves, F. "Ebenenteilung in Wirkungsbereiche." Zeitschrift für Kristallographie 76 (1931): 277-284.

Laves, F. "Ebenenteilung und Koordinationszahl." Zeitschrift für Kristallographie 78 (1931): 208-241.

Heesch, H. "Über topologisch gleichwertige Kristallbindungen." Zeitschrift für Kristallographie 84 (1933): 399-407.

 
New (latest additions/revisions first. A complete list is on the 'update history' page):

17 April 2014: Parquet Deformations - A change of presentation, with all material now on a single page, and additional text

11 April 2014: Pavement Tessellations - ‘Baldosa de Bilbao’ (Tile of Bilbao)
 
27 March 2014: Cluster Puzzles - Michael Angulo and George Luck puzzles added

19 March 2014. M. C. Escher Miscellany

5 March 2014: Pentagon Tilings - expanded following suggestions by Dale Walton

3 January 2014: Cairo tiling - Six fallacies
 
27 December 2013: Cairo tiling - Martin Gardner mystery resolved! The enigmatic reference to 'Moorish buildings' in his 'Scientific Amercan' artlce was of the Taj Mahal
 
23 December 2013: Pentagon Tilings. A study based on a pentagon tile as devised by Marjorie Rice, with added input by Vincent Kreugel

22 November 2013: Cluster Puzzles - Predecessors and successors to Escher's 'Plane Filling I' and 'Plane Filling II'
 
7 August 2013: Pavement Tessellations - Caribbean countries
 
25 June 2013: Pavement Tessellation - Innsbruck railway station, Germany
 
22 June 2013: Cairo tiling - 'Sightings in Books', a new page, with some material drawn from existing text, greatly revised and expanded
 
 
 

 
Comments