Stars (M. C. Escher)
|Artist||M. C. Escher|
|Dimensions||32 cm × 26 cm (13 in × 10 in)|
The print depicts a hollowed-out compound of three octahedra, a polyhedral compound composed of three regular octahedra, floating in space. Numerous other polyhedra and polyhedral compounds float in the background; the four largest are, on the upper left, the compound of cube and octahedron; on the upper right, the stella octangula; on the lower left, a compound of two cubes; and on the lower right, a solid version of the same octahedron 3-compound. The smaller polyhedra visible within the print also include all of the five Platonic solids and the rhombic dodecahedron.
Two chameleons are contained within the cage-like shape of the central compound; Escher writes that they were chosen as its inhabitants "because they are able to cling by their legs and tails to the beams of their cage as it swirls through space". The chameleon on the left sticks out his tongue, perhaps in commentary; Coxeter observes that the tongue has an unusual spiral-shaped tip.
Although most published copies of Stars are monochromatic, with white stars and chameleons on a black background, the copy in the National Gallery of Canada is tinted in different shades of turquoise, yellow, green, and pale pink.
The design for Stars was likely influenced by Escher's own interest in both geometry and astronomy, by a long history of using geometric forms to model the heavens, and by a drawing style used by Leonardo da Vinci. However, although the polyhedral shape depicted in Stars had been studied before in mathematics, it was most likely invented independently for this image by Escher without reference to those studies.
Escher's interest in geometry is well known, but he was also an avid amateur astronomer, and in the early 1940s became a member of the Dutch Association for Meteorology and Astronomy. He owned a 6 cm refracting telescope, and recorded several observations of binary stars.
The use of polyhedra to model heavenly bodies can be traced back to Plato, who wrote in Timaeus that the constellations were arranged in the form of a regular dodecahedron. Later, Johannes Kepler theorized that the distribution of distances of the planets from the sun could be explained by the shapes of the five Platonic solids. Escher, also, regularly depicted polyhedra in his artworks relating to astronomy and other worlds.
H. S. M. Coxeter reports that the shape of the central chameleon cage in Stars had previously been described, with a photograph of a model of the same shape, in 1900 by Max Brückner. However, Escher would not have been aware of this reference and Coxeter writes that "It is remarkable that Escher, without any knowledge of algebra or analytic geometry, was able to rediscover this highly symmetrical figure."
Martin Beech interprets the many polyhedral compounds within Stars as corresponding to double stars and triple star systems in astronomy. Beech writes that, for Escher, the mathematical orderliness of polyhedra depicts the "stability and timeless quality" of the heavens, and similarly Marianne L. Teuber writes that Stars "celebrates Escher's identification with Johannes Kepler's neo-Platonic belief in an underlying mathematical order in the universe".
Alternatively, Howard W. Jaffe interprets the polyhedral forms in Stars crystallographically, as "brilliantly faceted jewels" floating through space, with its compound polyhedra representing crystal twinning.
However, R. A. Dunlap points out the contrast between the order of the polyhedral forms and the more chaotic biological nature of the chameleons inhabiting them. In the same vein, Beech observes that the stars themselves convey tension between order and chaos: despite their symmetric shapes, the stars are scattered apparently at random, and vary haphazardly from each other. As Escher himself wrote about the central chameleon cage, "I shouldn't be surprised if it wobbles a bit."
A closely related woodcut, Study for Stars, completed in August 1948, depicts wireframe versions of several of the same polyhedra and polyhedral compounds, floating in black within a square composition, but without the chameleons. The largest polyhedron shown in Study for Stars, a stellated rhombic dodecahedron, is also one of two polyhedra depicted prominently in Escher's 1961 print Waterfall.
Escher's later work Four Regular Solids (Stereometric Figure) returned to the theme of polyhedral compounds, depicting a more explicitly Keplerian form in which the compound of the cube and octahedron is nested within the compound of the dodecahedron and icosahedron.
Collections and publications
- Locher, J. L. (2000), The Magic of M. C. Escher, Harry N. Abrams, Inc., p. 100, ISBN 0-8109-6720-0.
- Beech, Martin, Escher's Stars, Journal of the Royal Astronomical Society of Canada 86: 169–177, Bibcode:1992JRASC..86..169B.
- Hart, George W. (1996), "The Polyhedra of M.C. Escher", Virtual Polyhedra.
- Coxeter, H. S. M. (1985), A special book review: M. C. Escher: His life and complete graphic work, The Mathematical Intelligencer 7 (1): 59–69, doi:10.1007/BF03023010. Coxeter's analysis of Stars is on pp. 61–62.
- Escher, M. C. (2001), M.C. Escher, the graphic work, Taschen, p. v, ISBN 978-3-8228-5864-6.
- Stars, National Gallery of Canada, retrieved 2011-11-19.
- Calter, Paul (1998), "The Platonic Solids", Lecture Notes: Geometry in Art and Architecture, Dartmouth College.
- Teuber, M. L. (July 1974), Sources of ambiguity in the prints of Maurits C. Escher, Scientific American 231: 90–104, doi:10.1038/scientificamerican0774-90.
- Jaffe, Howard W. (1996), "About the frontispiece", Crystal Chemistry and Refractivity, Dover, p. vi, ISBN 978-0-486-69173-2.
- Dunlap, R. A. (1992), "Fivefold symmetry in the graphic art of M. C. Escher", in Hargittai, István, Fivefold Symmetry (2nd ed.), World Scientific, pp. 489–504, ISBN 978-981-02-0600-0.
- Locher (2000), p. 99.
- Clute, John; Grant, John (1999), The encyclopedia of fantasy (2nd ed.), Macmillan, p. 322, ISBN 978-0-312-19869-5.
- Artwork detail, Kemper Museum, retrieved 2011-11-19.