Звёзды Эшера: Полиэдрическая клетка и хамелеоны

Wood engraving print by M. C. Escher

Stars is a wood engraving print created by the Dutch artist M. C. Escher in 1948, depicting two chameleons in a polyhedral cage floating through space. The compound of three octahedra used for the central cage in Stars had been studied before in mathematics, and Escher likely learned of it from the book Vielecke und Vielflache by Max Brückner. Escher used similar compound polyhedral forms in several other works, including Crystal (1947), Study for Stars (1948), Double Planetoid (1949), and Waterfall (1961). 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. Commentators have interpreted the cage's compound shape as a reference to double and triple stars in astronomy, or to twinned crystals in crystallography. The image contrasts the celestial order of its polyhedral shapes with the more chaotic forms of biology. Prints of Stars belong to the permanent collections of major museums including the Rijksmuseum, the National Gallery of Art, and the National Gallery of Canada.

Stars is a wood engraving print; that is, it was produced by carving the artwork into the end grain of a block of wood (unlike a woodcut which uses the side grain), and then using this block to print the image. It was created by Escher in October 1948. Although most published copies of Stars are monochromatic, with white artwork against a black background, the copy in the National Gallery of Canada is tinted in different shades of turquoise, yellow, green, and pale pink. The chameleon on the left sticks out his tongue, perhaps in commentary; H. S. M. Coxeter observes that the tongue has an unusual spiral shaped tip. 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, nested within each other. Escher kept a model of this system of nested polyhedra, and regularly depicted polyhedra in his artworks relating to astronomy and other worlds. The stella octangula (Latin for "eight pointed star") in the upper right of Stars was first described by Pacioli, and later rediscovered by Kepler, who gave it its astronomical name. H. S. M. Coxeter reports that the shape of the central chameleon cage in Stars had previously been described in 1900 by Max Brückner, whose book Vielecke und Vielflache includes a photograph of a model of the same shape. Coxeter, believing that Escher was not aware of this reference, wrote "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. 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. 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. The stella octangula, a compound of two tetrahedra that appears in the upper right of Stars, also forms the central shape of another of Escher's astronomical works, Double Planetoid (1949).