''Stars'' is a

wood engraving Wood engraving is a printmaking technique, in which an artist works an image or ''matrix'' of images into a block of wood. Functionally a variety of woodcut, it uses relief printing, where the artist applies ink to the face of the block and pr ...

print Printing is the process for reproducing text and images using a master form or template Print or printing may also refer to: Publishing * Canvas print, the result of an image printed onto canvas which is often stretched, or gallery-wrapped, o ...

created by the Dutch artist

M. C. Escher Maurits Cornelis Escher (; 17 June 1898 – 27 March 1972) was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints. Despite wide popular interest, Escher was for most of his life neglected in th ...

in 1948, depicting two chameleons in a polyhedral cage floating through space. The

compound of three octahedra In mathematics, the compound of three octahedra or octahedron 3-compound is a polyhedral compound formed from three regular octahedra, all sharing a common center but rotated with respect to each other. Although appearing earlier in the mathemati ...

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 Johannes Max Brückner (5 August 1860 – 1 November 1934) was a German geometer, known for his collection of polyhedral models. Education and career Brückner was born in Hartau, in the Kingdom of Saxony, a town that is now part of Zittau, ...

. 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 Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, Drawing, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially re ...

. Commentators have interpreted the cage's compound shape as a reference to double and triple stars in

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

, or to twinned crystals in

crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wo ...

. The image contrasts the celestial order of its polyhedral shapes with the more chaotic forms of

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditar ...

. Prints of ''Stars'' belong to the permanent collections of major museums including the

Rijksmuseum The Rijksmuseum () is the national museum of the Netherlands dedicated to Dutch arts and history and is located in Amsterdam. The museum is located at the Museum Square in the borough of Amsterdam South, close to the Van Gogh Museum, the Sted ...

, the

National Gallery of Art The National Gallery of Art, and its attached Sculpture Garden, is a national art museum in Washington, D.C., United States, located on the National Mall, between 3rd and 9th Streets, at Constitution Avenue NW. Open to the public and free of ch ...

, and the

National Gallery of Canada The National Gallery of Canada (french: Musée des beaux-arts du Canada), located in the capital city of Ottawa, Ontario, is Canada's national art museum. The museum's building takes up , with of space used for exhibiting art. It is one of the ...

Description

''Stars'' is a

print; that is, it was produced by carving the artwork into the end grain of a block of wood (unlike a

woodcut Woodcut is a relief printing technique in printmaking Printmaking is the process of creating artworks by printing, normally on paper, but also on fabric, wood, metal, and other surfaces. "Traditional printmaking" normally covers only t ...

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 A monochrome or monochromatic image, object or palette is composed of one color (or values of one color). Images using only shades of grey are called grayscale (typically digital) or black-and-white (typically analog). In physics, monochro ...

, with white artwork against a black background, the copy in the

is tinted in different shades of turquoise, yellow, green, and pale pink. The print depicts a hollowed-out

, a

polyhedral compound In geometry, a polyhedral compound is a figure that is composed of several polyhedra sharing a common centre. They are the three-dimensional analogs of polygonal compounds such as the hexagram. The outer vertices of a compound can be connec ...

composed of three interlocking regular octahedra, floating in space. Numerous other

polyhedra In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on t ...

and polyhedral compounds float in the background; the four largest are, on the upper left, the

compound of cube and octahedron The compound of cube and octahedron is a polyhedron which can be seen as either a polyhedral stellation or a compound. Construction The 14 Cartesian coordinates of the vertices of the compound are. : 6: (±2, 0, 0), ( 0, ±2, 0), ( 0, 0, ±2) : ...

; on the upper right, the

stella octangula The stellated octahedron is the only stellation of the octahedron. It is also called the stella octangula (Latin for "eight-pointed star"), a name given to it by Johannes Kepler in 1609, though it was known to earlier geometers. It was depi ...

; 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 solid In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all e ...

s and the

rhombic dodecahedron In geometry, the rhombic dodecahedron is a convex polyhedron with 12 congruent rhombic faces. It has 24 edges, and 14 vertices of 2 types. It is a Catalan solid, and the dual polyhedron of the cuboctahedron. Properties The rhombic dodecahed ...

. In order to depict polyhedra accurately, Escher made models of them from cardboard. 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;

H. S. M. Coxeter Harold Scott MacDonald "Donald" Coxeter, (9 February 1907 – 31 March 2003) was a British and later also Canadian geometer. He is regarded as one of the greatest geometers of the 20th century. Biography Coxeter was born in Kensington t ...

observes that the tongue has an unusual

spiral In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point. Helices Two major definitions of "spiral" in the American Heritage Dictionary are:

Influences

Escher's interest in geometry is well known, but he was also an avid amateur astronomer, and in the early 1940s he became a member of the Dutch Association for Meteorology and Astronomy. He owned a 6 cm

refracting telescope A refracting telescope (also called a refractor) is a type of optical telescope that uses a lens as its objective to form an image (also referred to a dioptric telescope). The refracting telescope design was originally used in spyglasses and ...

, and recorded several observations of

binary star A binary star is a system of two stars that are gravitationally bound to and in orbit around each other. Binary stars in the night sky that are seen as a single object to the naked eye are often resolved using a telescope as separate stars, in ...

s. The use of polyhedra to model heavenly bodies can be traced back to

Plato Plato ( ; grc-gre, Πλάτων ; 428/427 or 424/423 – 348/347 BC) was a Greek philosopher born in Athens during the Classical period in Ancient Greece. He founded the Platonist school of thought and the Academy, the first institutio ...

, who in the ''

Timaeus Timaeus (or Timaios) is a Greek name. It may refer to: * ''Timaeus'' (dialogue), a Socratic dialogue by Plato *Timaeus of Locri, 5th-century BC Pythagorean philosopher, appearing in Plato's dialogue *Timaeus (historian) (c. 345 BC-c. 250 BC), Greek ...

'' identified the

regular dodecahedron A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces, 20 vertices, 30 edges, ...

with the shape of the heavens and its 12 faces with the constellations of the

zodiac The zodiac is a belt-shaped region of the sky that extends approximately 8° north or south (as measured in celestial latitude) of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The p ...

. Later, Johannes Kepler theorized that the distribution of distances of the planets from the sun could be explained by the shapes of the five

s, 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. Escher learned his wood engraving technique from

Samuel Jessurun de Mesquita Samuel Jessurun de Mesquita (6 June 1868 – 11 February 1944) was a Dutch graphic artist active in the years before the Second World War. His pupils included graphic artist M. C. Escher (1898–1972). A Sephardic Jew, in his old age he was sen ...

. He illustrated the octahedral compound of ''Stars'' in the beveled wire-frame style that had been used by

in his illustrations for

Luca Pacioli Fra Luca Bartolomeo de Pacioli (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accountin ...

's 1509 book, ''

De divina proportione ''Divina proportione'' (15th century Italian for ''Divine proportion''), later also called ''De divina proportione'' (converting the Italian title into a Latin one) is a book on mathematics written by Luca Pacioli and illustrated by Leonardo da ...

''. Coxeter's analysis of ''Stars'' is on pp. 61–62. The

(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.

reports that the shape of the central chameleon cage in ''Stars'' had previously been described in 1900 by

, 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." However,

George W. Hart George William Hart (born 1955) is an American sculptor and geometer. Before retiring, he was an associate professor of Electrical Engineering at Columbia University in New York City and then an interdepartmental research professor at Stony Br ...

has documented that Escher was familiar with Brückner's book and based much of his knowledge of stellated polyhedra and polyhedral compounds on it.

Analysis

Martin Beech interprets the many

s within ''Stars'' as corresponding to

double star In observational astronomy, a double star or visual double is a pair of stars that appear close to each other as viewed from Earth, especially with the aid of optical telescopes. This occurs because the pair either forms a binary star (i.e. a ...

s and

triple star systems Triple is used in several contexts to mean "threefold" or a "Treble (disambiguation), treble": Sports * Triple (baseball), a three-base hit * A basketball three-point field goal * A figure skating jump with three rotations * In bowling terms, thr ...

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 Crystal twinning occurs when two or more adjacent crystals of the same mineral are oriented so that they share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals that are tightly ...

. 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."

Related works

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 In geometry, the first stellation of the rhombic dodecahedron is a self-intersecting polyhedron with 12 faces, each of which is a non-convex hexagon. It is a stellation of the rhombic dodecahedron and has the same outer shell and the same visual ...

, is also one of two polyhedra depicted prominently in Escher's 1961 print ''

Waterfall A waterfall is a point in a river or stream where water flows over a vertical drop or a series of steep drops. Waterfalls also occur where meltwater drops over the edge of a tabular iceberg or ice shelf. Waterfalls can be formed in severa ...

''. The

, 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). The

in the upper left was used earlier by Escher, in ''Crystal'' (1947). 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

''Stars'' was used as

cover art Cover art is a type of artwork presented as an illustration or photograph on the outside of a published product such as a book (often on a dust jacket), magazine, newspaper (tabloid), comic book, video game ( box art), music album ( album ...

for the 1962 anthology ''Best Fantasy Stories'' edited by

Brian Aldiss Brian Wilson Aldiss (; 18 August 1925 – 19 August 2017) was an English writer, artist, and anthology editor, best known for science fiction novels and short stories. His byline reads either Brian W. Aldiss or simply Brian Aldiss, except for ...

, and for a 1971 Italian edition of occult guidebook '' The Morning of the Magicians''. It also formed the frontispiece for a 1996 textbook on

. As well as being exhibited in the

Escher Museum Escher in Het Paleis (''Escher in The Palace'') is a museum in The Hague, Netherlands, featuring the works of the Dutch graphical artist M. C. Escher. It is housed in the Lange Voorhout Palace since November 2002. In 2015 it was revealed that ...

, copies of ''Stars'' are in the permanent collections of the

Mildred Lane Kemper Art Museum The Mildred Lane Kemper Art Museum is an art museum located on the campus of Washington University in St. Louis, within the university's Sam Fox School of Design & Visual Arts. Founded in 1881 as the St. Louis School and Museum of Fine Arts, it wa ...

Boston Public Library The Boston Public Library is a municipal public library system in Boston, Massachusetts, United States, founded in 1848. The Boston Public Library is also the Library for the Commonwealth (formerly ''library of last recourse'') of the Common ...

, and the

References

{{M. C. Escher Works by M. C. Escher 1948 paintings Woodcuts Collections of the National Gallery of Art Collections of the National Gallery of Canada Prints of the Rijksmuseum Amsterdam Lizards in art