Stars (M. C. Escher)
Encyclopedia
Stars is a wood engraving
print
by the Dutch
artist
M. C. Escher
which was first printed in October 1948, depicting two chameleons in a polyhedral cage floating through space.
, 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 solid
s and the rhombic dodecahedron
.
Two chameleon
s 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.
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 6cm refracting telescope
, and recorded several observations of binary star
s.
The use of polyhedra to model heavenly bodies can be traced back to Plato
, who wrote in Timaeus
that the constellation
s 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 solid
s. Escher, also, regularly depicted polyhedra in his artworks relating to astronomy and other worlds.
Escher drew the octahedral compound of Stars in a beveled wire-frame style that was previously used by Leonardo da Vinci
in his illustrations for Luca Pacioli
's book, De divina proportione
.
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."
s within Stars as corresponding to double star
s 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".
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.
for the 1962 anthology
Best Fantasy Stories edited by Brian Aldiss
.
As well as being exhibited in the Escher Museum
, copies of Stars are in the permanent collections of the Mildred Lane Kemper Art Museum
and the National Gallery of Canada
.
Wood engraving
Wood engraving is a technique in printmaking where the "matrix" worked by the artist is a block of wood. It is a variety of woodcut and so a relief printing technique, where ink is applied to the face of the block and printed by using relatively low pressure. A normal engraving, like an etching,...
Old master print
An old master print is a work of art produced by a printing process within the Western tradition . A date of about 1830 is usually taken as marking the end of the period whose prints are covered by this term. The main techniques concerned are woodcut, engraving and etching, although there are...
by the Dutch
Dutch people
The Dutch people are an ethnic group native to the Netherlands. They share a common culture and speak the Dutch language. Dutch people and their descendants are found in migrant communities worldwide, notably in Suriname, Chile, Brazil, Canada, Australia, South Africa, New Zealand, and the United...
artist
Artist
An artist is a person engaged in one or more of any of a broad spectrum of activities related to creating art, practicing the arts and/or demonstrating an art. The common usage in both everyday speech and academic discourse is a practitioner in the visual arts only...
M. C. Escher
M. C. Escher
Maurits Cornelis Escher , usually referred to as M. C. Escher , was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs, and mezzotints...
which was first printed in October 1948, depicting two chameleons in a polyhedral cage floating through space.
Description
The print depicts a hollowed-out compound of three octahedraCompound 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 mathematical literature, it was rediscovered and popularized...
, a polyhedral compound
Polyhedral compound
A polyhedral compound is a polyhedron that is itself composed of several other polyhedra sharing a common centre. They are the three-dimensional analogs of polygonal compounds such as the hexagram....
composed of three regular octahedra
Octahedron
In geometry, an octahedron is a polyhedron with eight faces. A regular octahedron is a Platonic solid composed of eight equilateral triangles, four of which meet at each vertex....
, floating in space. Numerous other polyhedra
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
and polyhedral compounds float in the background; the four largest are, on the upper left, the compound of cube and octahedron
Compound of cube and octahedron
This polyhedron can be seen as either a polyhedral stellation or a compound.- As a compound :It can be seen as the compound of an octahedron and a cube...
; on the upper right, the stella octangula
Stella octangula
The stellated octahedron, or stella octangula, is the only stellation of the octahedron. It was named by Johannes Kepler in 1609, though it was known to earlier geometers...
; 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
Platonic solid
In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...
s and the rhombic dodecahedron
Rhombic dodecahedron
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 rhombic faces. It is an Archimedean dual solid, or a Catalan solid. Its dual is the cuboctahedron.-Properties:...
.
Two chameleon
Chameleon
Chameleons are a distinctive and highly specialized clade of lizards. They are distinguished by their parrot-like zygodactylous feet, their separately mobile and stereoscopic eyes, their very long, highly modified, and rapidly extrudable tongues, their swaying gait, the possession by many of a...
s 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
Criticism
Criticism is the judgement of the merits and faults of the work or actions of an individual or group by another . To criticize does not necessarily imply to find fault, but the word is often taken to mean the simple expression of an objection against prejudice, or a disapproval.Another meaning of...
; Coxeter observes that the tongue has an unusual spiral
Spiral
In mathematics, a spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.-Spiral or helix:...
-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
National Gallery of Canada
The National Gallery of Canada , located in the capital city Ottawa, Ontario, is one of Canada's premier art galleries.The Gallery is now housed in a glass and granite building on Sussex Drive with a notable view of the Canadian Parliament buildings on Parliament Hill. The acclaimed structure was...
is tinted in different shades of turquoise, yellow, green, and pale pink.
Influences
Refracting telescope
A refracting or refractor telescope is a type of optical telescope that uses a lens as its objective to form an image . The refracting telescope design was originally used in spy glasses and astronomical telescopes but is also used for long focus camera lenses...
, and recorded several observations of binary star
Binary star
A binary star is a star system consisting of two stars orbiting around their common center of mass. The brighter star is called the primary and the other is its companion star, comes, or secondary...
s.
The use of polyhedra to model heavenly bodies can be traced back to Plato
Plato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
, who wrote in Timaeus
Timaeus (dialogue)
Timaeus is one of Plato's dialogues, mostly in the form of a long monologue given by the title character, written circa 360 BC. The work puts forward speculation on the nature of the physical world and human beings. It is followed by the dialogue Critias.Speakers of the dialogue are Socrates,...
that the constellation
Constellation
In modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
s were arranged in the form of a regular dodecahedron. Later, Johannes Kepler
Johannes Kepler
Johannes Kepler was a German mathematician, astronomer and astrologer. A key figure in the 17th century scientific revolution, he is best known for his eponymous laws of planetary motion, codified by later astronomers, based on his works Astronomia nova, Harmonices Mundi, and Epitome of Copernican...
theorized that the distribution of distances of the planets from the sun could be explained by the shapes of the five Platonic solid
Platonic solid
In geometry, a Platonic solid is a convex polyhedron that is regular, in the sense of a regular polygon. Specifically, the faces of a Platonic solid are congruent regular polygons, with the same number of faces meeting at each vertex; thus, all its edges are congruent, as are its vertices and...
s. Escher, also, regularly depicted polyhedra in his artworks relating to astronomy and other worlds.
Escher drew the octahedral compound of Stars in a beveled wire-frame style that was previously used by Leonardo da Vinci
Leonardo da Vinci
Leonardo di ser Piero da Vinci was an Italian Renaissance polymath: painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, anatomist, geologist, cartographer, botanist and writer whose genius, perhaps more than that of any other figure, epitomized the Renaissance...
in his illustrations for Luca Pacioli
Luca Pacioli
Fra Luca Bartolomeo de Pacioli was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and seminal contributor to the field now known as accounting...
's book, De divina proportione
De divina proportione
De Divina Proportione is a famous book on mathematics written by Luca Pacioli around 1497 in Milan. Today only two versions of the original manuscript are believed still to exist...
.
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."
Analysis
Martin Beech interprets the many polyhedral compoundPolyhedral compound
A polyhedral compound is a polyhedron that is itself composed of several other polyhedra sharing a common centre. They are the three-dimensional analogs of polygonal compounds such as the hexagram....
s within Stars as corresponding to double star
Double star
In observational astronomy, a double star is a pair of stars that appear close to each other in the sky as seen from Earth when viewed through an optical telescope. This can happen either because the pair forms a binary star, i.e...
s and triple star systems
Multiple star
A multiple star consists of three or more stars which appear from the Earth to be close to one another in the sky. This may result from the stars being physically close and gravitationally bound to each other, in which case it is physical, or this closeness may be merely apparent, in which case...
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
Crystallography
Crystallography is the experimental science of the arrangement of atoms in solids. The word "crystallography" derives from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and grapho = write.Before the development of...
, as "brilliantly faceted jewels" floating through space, with its compound polyhedra representing crystal twinning
Crystal twinning
Crystal twinning occurs when two separate crystals share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals in a variety of specific configurations. A twin boundary or composition surface separates the two crystals....
.
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 stellatedStellation
Stellation is a process of constructing new polygons , new polyhedra in three dimensions, or, in general, new polytopes in n dimensions. The process consists of extending elements such as edges or face planes, usually in a symmetrical way, until they meet each other again...
rhombic dodecahedron
Rhombic dodecahedron
In geometry, the rhombic dodecahedron is a convex polyhedron with 12 rhombic faces. It is an Archimedean dual solid, or a Catalan solid. Its dual is the cuboctahedron.-Properties:...
, is also one of two polyhedra depicted prominently in Escher's 1961 print Waterfall
Waterfall (M. C. Escher)
Waterfall is a lithography print by the Dutch artist M. C. Escher which was first printed in October, 1961. It shows an apparent paradox where water from the base of a waterfall appears to run downhill before reaching the top of the 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
Stars was used as cover artCover art
Cover art is the illustration or photograph on the outside of a published product such as a book , magazine, comic book, video game , DVD, CD, videotape, or music album. The art has a primarily commercial function, i.e...
for the 1962 anthology
Anthology
An anthology is a collection of literary works chosen by the compiler. It may be a collection of poems, short stories, plays, songs, or excerpts...
Best Fantasy Stories edited by Brian Aldiss
Brian Aldiss
Brian Wilson Aldiss, OBE is an English author of both general fiction and science fiction. His byline reads either Brian W. Aldiss or simply Brian Aldiss. Greatly influenced by science fiction pioneer H. G. Wells, Aldiss is a vice-president of the international H. G. Wells Society...
.
As well as being exhibited in the Escher Museum
Escher Museum
The Escher Museum is a museum in The Hague, The Netherlands, featuring the works of the Dutch graphical artist M. C. Escher. This museum opened on 16 November 2002....
, copies of Stars are in the permanent collections of the Mildred Lane Kemper Art Museum
Mildred Lane Kemper Art Museum
The Mildred Lane Kemper Art Museum, sometimes referred to simply as "The Milly", 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. It was founded in 1881 as the St. Louis School and Museum of Fine Arts, and...
and the National Gallery of Canada
National Gallery of Canada
The National Gallery of Canada , located in the capital city Ottawa, Ontario, is one of Canada's premier art galleries.The Gallery is now housed in a glass and granite building on Sussex Drive with a notable view of the Canadian Parliament buildings on Parliament Hill. The acclaimed structure was...
.