Essays on Escher's 44 Tessellating Miscellany - An Introduction



1. Generalities
    1.1 Designs for Fabrics, c. 1926 and 1942-1943
    1.2 Designs for Intarsia Panels, 1940
    1.3 Designs for Carved Spheres, 1940, 1942 and 1943
    1.4 Designs for Tapestry, 1952
    1.5 Designs for Banknotes, 1950-1953
    1.6 Designs for Ceilings, 1951 and 1962
    1.7 Designs for Polyhedra, 1952
    1.8 Designs for Damask Tablecloths, Napkins and Finger Towels, 1954
    1.9 Designs for Murals, 1957
    1.10 Designs for Book Covers, 1958 and 1959
    1.11 Designs for Tiled Facades, 1959 and 1960
    1.12 Designs for Tiled Columns, 1959 and 1968
    1.13 Designs for Painted Columns, 1962

2. Background Details

3 . Book Abbreviations

Aside from Escher's numbered drawings and prints, there remains a considerable body of work of a substantial nature, undertaken on a variety of surfaces. This work takes the form of designs, generally commissions, for fabrics, intarsia panels, carved spheres, tapestries, banknotes, ceilings, polyhedra, wallpaper, tablecloths, murals, book covers, facades and columns.
    However, due to the somewhat fragmented nature of this work, the designs are not easily categorised for purposes of discussion (indeed, even if they are discussed at all), and so are thus generally relegated, unfairly, to the margins or footnotes with comments in brief, despite remaining worthy of a more detailed comment. Therefore, to rectify this shortcoming these are thus discussed in detail, in chronological order, away from the more ‘orderly‘ works of numbered drawings and catalogued prints. This takes the form of two parts. Firstly, a few generalities of each type, in which aspects in common are detailed, and, as many of the designs are interrelated; this thus saves unnecessary repetition on the individual works that follow. Secondly, in-depth discussions of each work, with a more detailed analysis per se. However, frustratingly, many works still await publication, of which these have been alluded to in various publications. Furthermore, some of the works are shown at too small a scale to see clearly their inherent properties. Consequently, the task of examining and discussing these are either impossible or impractical. Therefore, the following is of necessity occasionally patchy, albeit thorough as much as is possible in the circumstances. Occasionally, for the sake of a more structured entity, finished works are referred to and discussed even when no picture is available. Although this is not ideal, this occurs only when beyond all reasonable doubt the preparatory drawing is also the ‘same’ as the finished work, as with, for example the ceiling of [25].


1.1 DESIGNS FOR FABRICS, C 1924-1926 AND 1942-1943
Escher printed examples on fabrics from his tessellations in two distinct periods, around 1924-1926 and 1942-1943. For ease of reference these are thus discussed separately:

Around 1924-1926
Following some attempts at composing representational tessellations (drawings 1 and 2), likewise of 1924-1926, Escher then apparently printed three tessellation designs on fabric, a Dog-like ‘Lion’ (twice) and, a ‘Lion’ (twice), and a third tessellation, of ‘bats’, this having no definitive periodic drawing. All three motifs are of a fanciful nature, of which the resemblance to the above creatures is tenuous, to say the least. Indeed, the ‘lion’ nomenclature is stretched way beyond credulity. However, as these are of the earliest drawings, consequently not too much should be read into this as regards quality, as unavoidably these are essentially of an experimental nature concerning his first relatively ‘considered’ foray into tessellation.
    To repeat the motifs on the fabrics, Escher used a stamp of a number of individual blocks as the occasion demanded, and then appropriately repeated this, one motif at a time.
    Occasionally, the fabrics were exhibited, although not surprisingly, presumably due to the essentially unrecognisable creatures, these were not a success, as Escher himself stated in his 1941 article in De Delver. Consequently, as these efforts were so discouraging, Escher ceased any further attempts and returned to his more orthodox work.

Following a second considered study of tessellations, beginning in 1936, a second series of prints on fabric occurred in 1942-1943 with motifs of considerably better inherent quality. This consisted of three prints, based on drawings 56 (reptiles), 20 (fish), and 59 (two flatfish), all with a pronounced rotational theme, albeit the latter drawing is not of an inherent rotational nature. Furthermore, the latter two are not simply repeats of a tessellation design, as Escher shows these in compositional form.
    Regrettably, research is hindered by a lack of a complete inventory, as variations, involving drawing 59 is still to be published.


Upon the influential art critic G. H. ‘s-Gravesande having seen examples of Escher's work, this then led Escher to an introduction to H. T. Zweirs, who was one of the architects engaged in the building of the new Leiden Town Hall. This meeting then led to a substantial commission, in which he was asked to design decorative wall panels and a clock face (both in intarsia) for the council chamber, a wall panel (also in intarsia) for the mayor’s office and etched glass windows for book cabinets in the town clerks office.
    These were, excepting the glass windows, of a tessellating compositional nature, of decided complexity. For this he composed relatively large-scale designs in watercolour and gouache, with many more motifs than was his usual practise. However, not all of which were accepted.
    Regrettably, research is hindered by a lack of consistency in showing the various commissions, with various design drawings still to be published, along with the panels not being shown in context.


1.3 DESIGNS FOR CARVED SPHERES, 1940, 1942, 1943 and 1963
A possible application with periodic drawings is their suitability of being applied to three-dimensional models, namely with polyhedra and spheres. As this is a natural continuation of tessellating matters, this thus naturally aroused Escher's attention, although his interest in this field was relatively lightweight (at least in comparison to his tessellation work per se). This led to a series of four carved spheres, of 1940, 1942, 1943 and 1963, undertaken in the war years when Escher said that he found it difficult to concentrate on original tessellation work. However, this statement should not be taken literally, as arguably the most complex print of all, Verbum, was indeed composed during that period. Essentially, as the process of carving is undertaken in an mechanical (albeit obviously highly skilled) manner, with no originality of thought required once the design has been worked out, such craftsmanship was thus ideal for such troubled times. Indeed, after the war Escher did not return to this genre.
    A later sphere, of 1963, was not undertaken directly by Escher but was instead conceived as a commission from C.V.S. Roosevelt, carved from diagrams and instructions by the Japanese craftsman Masatoshi from instructions sent by Escher, of which he himself received one of the two spheres so carved.
    A feature of such models is that by their inherent nature they are suitable to show concepts of infinity, as the sphere (and therefore the motifs) can be turned all ways. In contrast, as the periodic drawings which of necessity can only show a fragment of their infinite nature, a sphere is thus more satisfying in these matters, as infinity can be captured with a finite number of motifs which can be portrayed in a more satisfying, self contained way when duly turned.
    A general discussion of the rationale behind the carved spheres by Escher's son, George, is in Art and Science, page 1, and a general discussion, with a quotation of Escher's, is on page 259.


Upon receiving a commission in 1949 from the weaver Edmond de Cneudt in Baarn, Escher composed a design to be executed as a tapestry. This shows a metamorphosis in a vertical orientation, essentially consisting of two distinct tessellations joined together by a fish motif with related elements to both drawings. In terms of quality, an exemplary metamorphosis occurs, the transformation taking place in a consistent manner with no abrupt changes that would spoil the effect. However, this is shown in the strictest sense for its own intrinsic sake, as a vertical transformation, from birds to fish to birds is an arbitrary composition. In contrast, the print Sky and Water I, of a similar concept, is more succinct, and therefore in that sense better.


Escher received a commission in July 1950 from the De Nederlandsche bank (The bank of the Netherlands) for a series of banknotes (of 10, 25 and 100 guilder, with a later one of 50 guilder), to be printed by the engravers J. Enschedé and Sons. This took up a great deal of Escher's time, of which he worked on this at an intermittent basis from 1950-1953.
    Escher composed designs for the obverse, reverse and watermarks, with a variety of orthodox artwork of a typical nature for banknotes along with tessellation. The obverse took the form of portraits of eminent Dutch and Dutch/Belgian scientists, Antoni van Leeuwenhoek (1632-1723), Christiaan Huygens (1629-1695) and Simon Stevin (1548-1620) along with their achievements and scientific implements. The reverse is less structured, containing a pictorial miscellany of Leeuwenhoek and Stevin’s achievements, whilst Huygens’ note has a variation of drawing 55 [Fish], of November 1942. The latter also had as a watermark a variation of drawing 44 [Birds], of 1941, of which this was apparently chosen without a specific reference to Huygens achievements. A further proposed watermark is a variation of drawing 12 [Butterfly], of which the butterfly motif is transformed into a ‘bee’. However, despite strenuous efforts on Escher's part to accommodate the necessarily strict procedures for the print process, the commission was eventually withdrawn.
    Concept drawings for these are shown in Magic Mirror, page 62 and Visions of Symmetry, as A4-A11, pages 231-233, where proposed ribbon-like designs are shown.
    Regrettably, research is hindered by the paucity of both pictures and details surrounding the banknotes, with only Ernst discussing and showing examples of this per se, and furthermore the text is of a lightweight nature, of a single paragraph.


Escher received two distinct commissions for ceiling designs, of which for purposes of discussion are thus detailed separately.

Escher received a commission from the Phillips company in Eindhoven in 1951, to design a large scale work for the ceiling in their original 1891 factory building, to show modern lighting engineering.

Escher received a commission from the Secretary General of the Dutch Ministry of Agriculture and Fisheries in The Hague in 1962. The ceiling for the Secretary General took the form of a large panel, 4 x 6 metres, of stretched vellum (page 113) containing appropriate (fish and bird) motifs that from the design that Escher composed. For this, hired painters then of necessity undertook the commission, due to Escher’s poor health.


In the spring of 1952 for a brief period, Escher turned his attention to the application of tessellations to polyhedra, constructing cardboard models of his designs. Perhaps somewhat surprisingly, despite tessellations having a natural association with polyhedra, Escher had previously essentially neglected this aspect. Indeed, upon completion he never returned to their study per se.
    Essentially, the task of adapting tessellations to polyhedra is a simple process, as in principle a design based on, say; equilateral triangles can thus be applied to a tetrahedron or octahedron by simply cutting out an appropriate net. However, this is not invariably so, as on occasions the symmetry of the underlying tessellation, whilst suitable for a given polyhedron will not be found to be so where the motifs are then included.
    Schattschneider and Walker in Kaleidocycles show some examples of what Escher could have achieved in this field, where they adapt his designs to an assortment of polyhedra.


Unfortunately, the designs for the above, commissioned from the E. J. F. van Dissel company of Eindhoven in 1954, have received scant coverage, with no published material depicting the table ware. All that is available is a solitary concept sketch in Visions of Symmetry, page 308, and so, consequently, an in-depth discussion is not feasible. Consequently, research is hindered.


Escher received a commission in late 1957 from the city of Utrecht for two murals in the main hall of the third municipal cemetery in the family waiting room and the aula. Unfortunately, the design for the family waiting room has received scant coverage, only available as a drawing (albeit of a finished nature), shown in Visions of Symmetry, page 234. Presumably, this is then simply scaled up. The design for the aula, although scant, is nonetheless acceptable for detailed discussion purposes. For this, he used fish motifs to show an appropriate concept for the cemetery, symbolising birth, life and death with a series of fish reducing in size in spiral form, of which he undertook the task of this himself. Such a concept and similarity can be seen in other prints of the same period, as with Whirlpools.


1.10 DESIGNS FOR BOOK COVERS, 1958 AND 1959 (2)
Escher designed three book covers, of which two were for his own books, Regelmatige vlakverderling of 1958, commissioned by the De Roos foundation and Grafiek en tekeningen of 1959. A third book, also of 1959 Nieuw Leerbroek Der Algebra I is one of a series of mathematical books for schools published by J. B. Woulters, Groningen, shows an apparently specially designed composition.
    Examples of the front covers of Grafiek en tekeningen and Nieuw Leerbroek Der Algebra I are shown in Visions of Symmetry, pages 276 and 273 respectively.


Escher received two distinct commissions that although are very near in chronology and are not related. Consequently, these are discussed separately.

A noticeable feature is the scale of this commission, of 5 x 14 metres, for the entrance to the Vrijzinnig-Christelijk Lyceum (Liberal Christian Lyceum), The Hague.

Unfortunately, the tile tableau for the façade of a private house in Amsterdam has received scant attention, the only appearance being in Visions of Symmetry, page 306, and furthermore, the photograph, although clear, is of such a small scale that the detail is not readily discernable.


Escher received commissions in two distinct, unrelated periods, of 1959 and 1968 specifically for tiled columns. As these are distinct, they are thus discussed separately.

Escher received a commission in c. November 1959, from the Nieuwe Meisjesschool (New Girls’ School) renamed Johanna Westermanschool, in The Hague, for a series of designs suitable for three columns (each column being 34 cm in diameter, 250 cm tall). For this, the periodic drawings were thus essentially wrapped around a cylinder, from which he then had to find a square unit that contained all the elements of both black and white motifs that would repeat when so manufactured. This took the form of manufactured curved tiles (by the De Porceleyne Fles Company in Delft) containing all the necessary tessellation elements on a single tile.
    For this, he chose appropriate designs in a considered way, these showing principles of mathematics per se, showing aspects of symmetry and not concepts of association of the motifs. This took the form of translation, rotation and glide reflection symmetries, using drawings 74 [Birds], 96 [Swan] and 104 [Lizard] respectively; the latter almost certainly designed especially for the commission, albeit not strictly required, as arguably a better lizard was available (drawing 15).
    Escher was notably displeased with the lack of care in which the tiles were assembled, of which misalignments can be seen in the detailed pictures (below), and therefore tried to have these redone, without success.
    All three of the columns are discussed and pictured in situ in an article by Marjorie Senechal, ‘Escher Designs on Surfaces’ in Art and Science, pages 97-109.
    Escher briefly mentions the commission in a letter to his son Arthur in Life and Work, pages 91-92.

Escher received a commission for the New Lyceum, Baarn, in 1968 for tiled columns.
    Unfortunately, this has received scant attention, with only a solitary picture, in Visions of Symmetry, pages 317-318 only showing detail of the columns, and not them in situ. Consequently, it is less clear as to whether these were deliberately designed as according to symmetry principles.
    The columns are 60 cm in diameter, height 260 cm.
    Escher briefly mentions the commission in a letter, of May 1968, to his son Arthur, in Life and Work, page 126.


Escher received a commission from the Provinciale Waterstaat en Planologische Dienst (Provincial Bureau of Water Management and Planning), Haarlem, for a painted column. This was to be based upon a water theme, with appropriate motifs, of which all four of the drawings (111-114) underlying this were specially designed for this express purpose. Although these are not of his best work in terms of inherent quality, they retain much of merit despite their ‘forced’ nature. The column is pictured on page 260.


2 Background Details
Each work is discussed here in an individual manner, as a work of art in its own right. Occasionally, where these are formed as part of a concerted series, this aspect is thus noted. Regrettably, research is hindered as not all of the finished works have been published (these made known through drawings only), and furthermore on occasions the pictures that are shown can be at too small a scale to see clearly their intricacies. However, although not ideal, in practise such drawbacks can generally be accommodated.
    For reference purposes, each work is discussed in two distinct parts, with background details (below) followed by an in-depth discussion.

• Numbered and titled. These are numbered as they appear in chronological order, the numbers not appearing to any published catalogue of Escher's works. Furthermore, the titles are also of my own devising, where possible retaining Schattschneider’s nomenclature in Visions of Symmetry.

• Year of creation.

• Medium, if appropriate.·

• Discussed in.
Where examples of the work are discussed, the sources are given. Regrettably, as detailed above, very little discussion is to be found, and where such examples do indeed occur all too often are of a lightweight nature, frequently of only one or two lines. Consequently, I make the distinction between mere mentions of the works and discussions in the proper sense of the word of the work. Even so, due to relative paucity, I nonetheless include on occasions text that ideally would not normally be included in the above category.

• Pictured in.
Where a work is pictured, the sources are given. As a rule, the picture size can vary, and where fine detail is a requisite, some are thus naturally superior to others. In addition, where a picture is shown in monochrome this is thus stated.

• Based on.
The drawing number that the work uses is given, along with its title in square brackets as given by Schattschneider, followed by the date. Occasionally, no numbered drawing exists, of which this is thus stated as ‘unknown’.

• Concept drawing.
Occasionally, a concept drawing/s is shown, of which the source is thus given.

3 Abbreviations for Book Titles
The following abbreviations for book titles (based on their title in English) are used:

Regular Division: Regelmatige vlakverderling (Regular Division of the Plane, 1958)

Graphic Work: Grafiek en tekeningen (The Graphic Work of M.C. Escher, 1960)

World: De werelden van M.C. Escher (The World of M.C. Escher, 1971)

Magic Mirror: De toverspiegel van M.C. Escher (The Magic Mirror of M.C. Escher, 1976)

Life and Work: Leven en werk van M.C. Escher (M.C. Escher, His Life and Complete Graphic Work, 1982)

Art and Science: M.C. Escher: Art and Science, 1986

Escher on Escher: Het oneindige: M.C. Escher over eigen werk (Escher on Escher: Exploring the Infinite, 1989)

Visions of Symmetry: Visions of Symmetry. Notebooks, Periodic Drawings, and Related Work of M.C. Escher, 1990

Magic: The Magic of M.C. Escher, 2000

Legacy: M.C. Escher's Legacy, 2005


Last updated 14 November 2005