Pentagram
Encyclopedia
Regular pentagram

A pentagram
Type Star polygon
Edge
Edge (geometry)
In geometry, an edge is a one-dimensional line segment joining two adjacent zero-dimensional vertices in a polygon. Thus applied, an edge is a connector for a one-dimensional line segment and two zero-dimensional objects....

s and vertices
Vertex (geometry)
In geometry, a vertex is a special kind of point that describes the corners or intersections of geometric shapes.-Of an angle:...

5
Schläfli symbol {5/2}
Coxeter–Dynkin diagram
Symmetry group D5 (Order 10)
Internal angle
Internal angle
In geometry, an interior angle is an angle formed by two sides of a polygon that share an endpoint. For a simple, convex or concave polygon, this angle will be an angle on the 'inner side' of the polygon...

(degree
Degree (angle)
A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...

s)
36° (108°)

A pentagram (sometimes known as a pentalpha or pentangle or, more formally, as a star pentagon) is the shape of a five-pointed star
Five-pointed star
A five-pointed star is a very common ideogram throughout the world. If the colinear edges are joined together a pentagram is produced, which is the simplest of the unicursal star polygons, and a symbol of mystical and magical significance....

drawn with five straight strokes. The word pentagram comes from the Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

word πεντάγραμμον (pentagrammon), a noun
Noun
In linguistics, a noun is a member of a large, open lexical category whose members can occur as the main word in the subject of a clause, the object of a verb, or the object of a preposition .Lexical categories are defined in terms of how their members combine with other kinds of...

form of πεντάγραμμος (pentagrammos) or πεντέγραμμος (pentegrammos), a word meaning roughly "five-lined" or "five lines", from πέντε (pente), "five" + γραμμή (grammē), "line".

Pentagrams were used symbolically in ancient Greece
Ancient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...

and Babylonia
Babylonia
Babylonia was an ancient cultural region in central-southern Mesopotamia , with Babylon as its capital. Babylonia emerged as a major power when Hammurabi Babylonia was an ancient cultural region in central-southern Mesopotamia (present-day Iraq), with Babylon as its capital. Babylonia emerged as...

, and are used today as a symbol of faith by many Wicca
Wicca
Wicca , is a modern Pagan religious movement. Developing in England in the first half of the 20th century, Wicca was popularised in the 1950s and early 1960s by a Wiccan High Priest named Gerald Gardner, who at the time called it the "witch cult" and "witchcraft," and its adherents "the Wica."...

ns, akin to the use of the cross
Cross
A cross is a geometrical figure consisting of two lines or bars perpendicular to each other, dividing one or two of the lines in half. The lines usually run vertically and horizontally; if they run obliquely, the design is technically termed a saltire, although the arms of a saltire need not meet...

by Christians and the Star of David
Star of David
The Star of David, known in Hebrew as the Shield of David or Magen David is a generally recognized symbol of Jewish identity and Judaism.Its shape is that of a hexagram, the compound of two equilateral triangles...

by Jews. The pentagram has magical
Magic (paranormal)
Magic is the claimed art of manipulating aspects of reality either by supernatural means or through knowledge of occult laws unknown to science. It is in contrast to science, in that science does not accept anything not subject to either direct or indirect observation, and subject to logical...

associations, and many people who practice Neopagan
Neopaganism
Neopaganism is an umbrella term used to identify a wide variety of modern religious movements, particularly those influenced by or claiming to be derived from the various pagan beliefs of pre-modern Europe...

faiths wear jewelry incorporating the symbol. Christians
Christianity
Christianity is a monotheistic religion based on the life and teachings of Jesus as presented in canonical gospels and other New Testament writings...

once more commonly used the pentagram to represent the five wounds of Jesus
Holy Wounds
The Five Holy Wounds or Five Sacred Wounds refer to what are believed to be the five piercing wounds that was suffered during the crucifixion of Jesus....

. The pentagram has associations with Freemasonry
Freemasonry
Freemasonry is a fraternal organisation that arose from obscure origins in the late 16th to early 17th century. Freemasonry now exists in various forms all over the world, with a membership estimated at around six million, including approximately 150,000 under the jurisdictions of the Grand Lodge...

and is also utilized by other belief systems.

The word "pentacle
Pentacle
A pentacle is an amulet used in magical evocation, generally made of parchment, paper or metal , on which the symbol of a spirit or energy being evoked is drawn. It is often worn around the neck, or placed within the triangle of evocation...

" is sometimes used synonymously with "pentagram", and this usage is borne out by the Oxford English Dictionary, although that work specifies that a circumscription makes the shape more particularly a pentacle. Wiccans and Neo-pagans often make use of this more specific definition for a pentagram enclosed in a circle.

### Sumer

The first known uses of the pentagram are found in Mesopotamia
Mesopotamia
Mesopotamia is a toponym for the area of the Tigris–Euphrates river system, largely corresponding to modern-day Iraq, northeastern Syria, southeastern Turkey and southwestern Iran.Widely considered to be the cradle of civilization, Bronze Age Mesopotamia included Sumer and the...

n writings dating to about 3000 BC.
The Sumer
Sumer
Sumer was a civilization and historical region in southern Mesopotamia, modern Iraq during the Chalcolithic and Early Bronze Age....

ian pentagrams served as pictograms for the word "UB" meaning "corner, angle, nook; a small room, cavity, hole; pitfall," suggesting something very similar to the pentemychos (see below on the Pythagorean use for what pentemychos means). In René Labat's index system of Sumer
Sumer
Sumer was a civilization and historical region in southern Mesopotamia, modern Iraq during the Chalcolithic and Early Bronze Age....

ian hieroglyphs/pictogram
Pictogram
A pictograph, also called pictogram or pictogramme is an ideogram that conveys its meaning through its pictorial resemblance to a physical object. Pictographs are often used in writing and graphic systems in which the characters are to considerable extent pictorial in appearance.Pictography is a...

s it is shown with two points up.
In the Babylonia
Babylonia
Babylonia was an ancient cultural region in central-southern Mesopotamia , with Babylon as its capital. Babylonia emerged as a major power when Hammurabi Babylonia was an ancient cultural region in central-southern Mesopotamia (present-day Iraq), with Babylon as its capital. Babylonia emerged as...

n context, the edges of the pentagram were probably orientations: forward, backward, left, right, and "above". These directions also had an astrological
Astrology
Astrology consists of a number of belief systems which hold that there is a relationship between astronomical phenomena and events in the human world...

meaning, representing the five planets Jupiter
Jupiter
Jupiter is the fifth planet from the Sun and the largest planet within the Solar System. It is a gas giant with mass one-thousandth that of the Sun but is two and a half times the mass of all the other planets in our Solar System combined. Jupiter is classified as a gas giant along with Saturn,...

, Mercury
Mercury (planet)
Mercury is the innermost and smallest planet in the Solar System, orbiting the Sun once every 87.969 Earth days. The orbit of Mercury has the highest eccentricity of all the Solar System planets, and it has the smallest axial tilt. It completes three rotations about its axis for every two orbits...

, Mars
Mars
Mars is the fourth planet from the Sun in the Solar System. The planet is named after the Roman god of war, Mars. It is often described as the "Red Planet", as the iron oxide prevalent on its surface gives it a reddish appearance...

and Saturn
Saturn
Saturn is the sixth planet from the Sun and the second largest planet in the Solar System, after Jupiter. Saturn is named after the Roman god Saturn, equated to the Greek Cronus , the Babylonian Ninurta and the Hindu Shani. Saturn's astronomical symbol represents the Roman god's sickle.Saturn,...

, and Venus
Venus
Venus is the second planet from the Sun, orbiting it every 224.7 Earth days. The planet is named after Venus, the Roman goddess of love and beauty. After the Moon, it is the brightest natural object in the night sky, reaching an apparent magnitude of −4.6, bright enough to cast shadows...

as the "Queen of Heaven" (Ishtar
Ishtar
Ishtar is the Assyrian and Babylonian goddess of fertility, love, war, and sex. She is the counterpart to the Sumerian Inanna and to the cognate north-west Semitic goddess Astarte.-Characteristics:...

) above.

### Pythagoreans

The Pythagoreans called the pentagram ὑγιεία Hugieia ("health"; also the Greek goddess of health, Hygieia
Hygieia
In Greek and Roman mythology, Hygieia , was a daughter of the god of medicine, Asclepius. She was the goddess/personification of health , cleanliness and sanitation. She also played an important part in her father's cult...

), and saw in the pentagram a mathematical perfection (see Geometry section below).

The ancient Pythagorean pentagram, with two legs up, represented the Pentemychos (πεντέμυχος "of five sanctuaries"), a cosmogony
Cosmogony
Cosmogony, or cosmogeny, is any scientific theory concerning the coming into existence or origin of the universe, or about how reality came to be. The word comes from the Greek κοσμογονία , from κόσμος "cosmos, the world", and the root of γίνομαι / γέγονα "to be born, come about"...

written by Pythagoras'
Pythagoras
Pythagoras of Samos was an Ionian Greek philosopher, mathematician, and founder of the religious movement called Pythagoreanism. Most of the information about Pythagoras was written down centuries after he lived, so very little reliable information is known about him...

teacher and friend Pherecydes of Syros
Pherecydes of Syros
Pherecydes of Syros was a Greek thinker from the island of Syros, of the 6th century BC. Pherecydes authored the Pentemychos or Heptamychos, one of the first attested prose works in Greek literature, which formed an important bridge between mythic and pre-Socratic thought.- Life :Very little is...

. It was the "island" or "cave" where the first pre-cosmic-offspring had to be put in order for the cosmos
Cosmos
In the general sense, a cosmos is an orderly or harmonious system. It originates from the Greek term κόσμος , meaning "order" or "ornament" and is antithetical to the concept of chaos. Today, the word is generally used as a synonym of the word Universe . The word cosmos originates from the same root...

to appear: "the divine products of Chronos'
Chronos
In Greek mythology, Chronos in pre-Socratic philosophical works is said to be the personification of time. His name in Greek means "time" and is alternatively spelled Chronus or Khronos.Chronos was imagined as an incorporeal god, serpentine in form, with three heads—those of a man, a bull, and...

seed [σπέρμα spérma], when disposed in five recesses, were called Πεντέμυχος (Pentemuxos)".

### Wu Xing

Wu Xing , the five phases, or five elements, is an ancient Chinese mnemonic
Mnemonic
A mnemonic , or mnemonic device, is any learning technique that aids memory. To improve long term memory, mnemonic systems are used to make memorization easier. Commonly encountered mnemonics are often verbal, such as a very short poem or a special word used to help a person remember something,...

and symbolic figure widely known in East Asia and used traditionally in applications such as medicine
Traditional Chinese Medicine refers to a broad range of medicine practices sharing common theoretical concepts which have been developed in China and are based on a tradition of more than 2,000 years, including various forms of herbal medicine, acupuncture, massage , exercise , and dietary therapy...

, acupuncture
Acupuncture
Acupuncture is a type of alternative medicine that treats patients by insertion and manipulation of solid, generally thin needles in the body....

, feng shui
Feng shui
Feng shui ' is a Chinese system of geomancy believed to use the laws of both Heaven and Earth to help one improve life by receiving positive qi. The original designation for the discipline is Kan Yu ....

, and Taoism
Taoism
Taoism refers to a philosophical or religious tradition in which the basic concept is to establish harmony with the Tao , which is the mechanism of everything that exists...

. They are similar to the ancient Greek elements, with more emphasis on their cyclic transformation than on their material aspects. The five phases are: Fire (火 huǒ), Earth (土 ), Metal (金 jīn), Water (水 shuǐ), and Wood (木 ).

The vector
Arrow (symbol)
An arrow is a graphical symbol such as → or ←, used to point or indicate direction, being in its simplest form a line segment with a triangle affixed to one end, and in more complex forms a representation of an actual arrow...

s of the overcoming or controlling cycle visually form a pentagram which is commonly incorporated into depictions. Generative and destructive cycles are shown as clockwise and counter-clockwise circular motion.
controlling cycle:
generative cycle:
destructive cycle:

## European occultism

Heinrich Cornelius Agrippa
Heinrich Cornelius Agrippa
Heinrich Cornelius Agrippa von Nettesheim was a German magician, occult writer, theologian, astrologer, and alchemist.-Life:Agrippa was born in Cologne in 1486...

and others perpetuated the popularity of the pentagram as a magic symbol, keeping the Pythagorean attributions of elements to the five points. By the mid-19th century a further distinction had developed amongst occultists regarding the pentagram's orientation. With a single point upwards it depicted spirit presiding over the four elements of matter, and was essentially "good". However, the influential writer Eliphas Levi
Eliphas Levi
Eliphas Lévi, born Alphonse Louis Constant , was a French occult author and purported magician."Eliphas Lévi," the name under which he published his books, was his attempt to translate or transliterate his given names "Alphonse Louis" into Hebrew although he was not Jewish.His second wife was...

called it evil whenever the symbol appeared the other way up.
"A reversed pentagram, with two points projecting upwards, is a symbol of evil and attracts sinister forces because it overturns the proper order of things and demonstrates the triumph of matter over spirit. It is the goat of lust attacking the heavens with its horns, a sign execrated by initiates."
"The flaming star, which, when turned upside down, is the hierolgyphic [sic] sign of the goat of Black Magic, whose head may be drawn in the star, the two horns at the top, the ears to the right and left, the beard at the bottom. It is the sign of antagonism and fatality. It is the goat of lust attacking the heavens with its horns."
"Let us keep the figure of the Five-pointed Star always upright, with the topmost triangle pointing to heaven, for it is the seat of wisdom, and if the figure is reversed, perversion and evil will be the result."

### Bahá'í Faith

In the Bahá'í Faith, the star is known as the Haykal , and it was initiated and established by the Báb
Báb
Siyyid `Alí Muḥammad Shírází was the founder of Bábism, and one of three central figures of the Bahá'í Faith. He was a merchant from Shíráz, Persia, who at the age of twenty-four claimed to be the promised Qá'im . After his declaration he took the title of Báb meaning "Gate"...

. The Báb and Bahá'u'lláh
Bahá'u'lláh
Bahá'u'lláh , born ' , was the founder of the Bahá'í Faith. He claimed to be the prophetic fulfilment of Bábism, a 19th-century outgrowth of Shí‘ism, but in a broader sense claimed to be a messenger from God referring to the fulfilment of the eschatological expectations of Islam, Christianity, and...

wrote various works in the form of a pentagram.

### Christianity

The pentagram is used as a Christian symbol for the five sense
Sense
Senses are physiological capacities of organisms that provide inputs for perception. The senses and their operation, classification, and theory are overlapping topics studied by a variety of fields, most notably neuroscience, cognitive psychology , and philosophy of perception...

s,
Medieval Christians believed that the "pentalpha" symbolizes the five wounds of Christ. The pentagram was believed to protect against demons.

The pentagram figured in a heavily symbolic Arthurian
King Arthur
King Arthur is a legendary British leader of the late 5th and early 6th centuries, who, according to Medieval histories and romances, led the defence of Britain against Saxon invaders in the early 6th century. The details of Arthur's story are mainly composed of folklore and literary invention, and...

romance: it appears on the shield of Sir Gawain in the 14th century poem Sir Gawain and the Green Knight
Sir Gawain and the Green Knight
Sir Gawain and the Green Knight is a late 14th-century Middle English alliterative romance outlining an adventure of Sir Gawain, a knight of King Arthur's Round Table. In the poem, Sir Gawain accepts a challenge from a mysterious warrior who is completely green, from his clothes and hair to his...

. As the poet explains, the five points of the star each have five meanings: they represent the five senses, the five fingers, the five wounds of Christ
Christ
Christ is the English term for the Greek meaning "the anointed one". It is a translation of the Hebrew , usually transliterated into English as Messiah or Mashiach...

, the five joys that Mary had of Jesus (the Annunciation
Annunciation
The Annunciation, also referred to as the Annunciation to the Blessed Virgin Mary or Annunciation of the Lord, is the Christian celebration of the announcement by the angel Gabriel to Virgin Mary, that she would conceive and become the mother of Jesus the Son of God. Gabriel told Mary to name her...

, the Nativity
Nativity of Jesus
The Nativity of Jesus, or simply The Nativity, refers to the accounts of the birth of Jesus in two of the Canonical gospels and in various apocryphal texts....

, the Resurrection
Resurrection of Jesus
The Christian belief in the resurrection of Jesus states that Jesus returned to bodily life on the third day following his death by crucifixion. It is a key element of Christian faith and theology and part of the Nicene Creed: "On the third day he rose again in fulfillment of the Scriptures"...

, the Ascension, and the Assumption
Assumption of Mary
According to the belief of Christians of the Roman Catholic Church, Eastern Orthodoxy, Oriental Orthodoxy, and parts of the Anglican Communion and Continuing Anglicanism, the Assumption of Mary was the bodily taking up of the Virgin Mary into Heaven at the end of her life...

), and the five virtues of knighthood which Gawain hopes to embody: noble generosity, fellowship, purity, courtesy, and compassion.

### Mormonism

The Church of Jesus Christ of Latter-day Saints began using both upright and inverted five-pointed stars in Temple architecture, dating from the Nauvoo Illinois Temple
Nauvoo Illinois Temple
The Nauvoo Illinois Temple is the 113th dedicated temple of The Church of Jesus Christ of Latter-day Saints. It is the third such temple that has been built in Illinois ....

, which was dedicated on April 30, 1846. Other temples decorated with five-pointed stars in both orientations include the Salt Lake Temple
Salt Lake Temple
The Salt Lake Temple is the largest and best-known of more than 130 temples of The Church of Jesus Christ of Latter-day Saints. It is the sixth temple built by the church, requiring 40 years to complete, and the fourth operating temple built since the Mormon exodus from Nauvoo,...

, and the Logan Temple. These symbols derived from traditional Morning Star pentagrams that are no longer commonly used by other Christian denominations.

### Neopaganism

Many Neopagans
Neopaganism
Neopaganism is an umbrella term used to identify a wide variety of modern religious movements, particularly those influenced by or claiming to be derived from the various pagan beliefs of pre-modern Europe...

, especially Wicca
Wicca
Wicca , is a modern Pagan religious movement. Developing in England in the first half of the 20th century, Wicca was popularised in the 1950s and early 1960s by a Wiccan High Priest named Gerald Gardner, who at the time called it the "witch cult" and "witchcraft," and its adherents "the Wica."...

ns, use the pentagram as a symbol of faith similar to the Christian
Christian
A Christian is a person who adheres to Christianity, an Abrahamic, monotheistic religion based on the life and teachings of Jesus of Nazareth as recorded in the Canonical gospels and the letters of the New Testament...

cross
Cross
A cross is a geometrical figure consisting of two lines or bars perpendicular to each other, dividing one or two of the lines in half. The lines usually run vertically and horizontally; if they run obliquely, the design is technically termed a saltire, although the arms of a saltire need not meet...

or the Jewish Star of David
Star of David
The Star of David, known in Hebrew as the Shield of David or Magen David is a generally recognized symbol of Jewish identity and Judaism.Its shape is that of a hexagram, the compound of two equilateral triangles...

. Its religious symbolism is commonly explained by reference to the neo-Pythagorean understanding that the five vertices of the pentagram represent the four elements with the addition of Spirit as the uppermost point. As a representation of the elements, the pentagram is involved in the Wiccan practice of summoning the elemental
Elemental
An elemental is a mythological being first appearing in the alchemical works of Paracelsus in the 16th century. Traditionally, there are four types:*gnomes, earth elementals*undines , water elementals*sylphs, air elementals...

spirits of the four directions at the beginning of a ritual.

The outer circle of the circumscribed pentagram is sometimes interpreted as binding the elements together or bringing them into harmony with each other. The Neopagan pentagram is generally displayed with one point up, partly because of the "inverted" goat's head pentagram's association with Satanism; however, within traditional forms of Wicca
Wicca
Wicca , is a modern Pagan religious movement. Developing in England in the first half of the 20th century, Wicca was popularised in the 1950s and early 1960s by a Wiccan High Priest named Gerald Gardner, who at the time called it the "witch cult" and "witchcraft," and its adherents "the Wica."...

a pentagram (no circle) with two points up is associated with the Second Degree Initiation
Initiation
Initiation is a rite of passage ceremony marking entrance or acceptance into a group or society. It could also be a formal admission to adulthood in a community or one of its formal components...

and in this way differs from the encircled pentacle inverted of Satanism.

Because of a perceived association with Satanism and also because of negative societal attitudes towards Neopagan religions and the "occult
Occult
The word occult comes from the Latin word occultus , referring to "knowledge of the hidden". In the medical sense it is used to refer to a structure or process that is hidden, e.g...

", many United States schools have sought to prevent students from displaying the pentagram on clothing or jewelry. In public schools, such actions by administrators have been determined to be in violation of students' First Amendment
First Amendment to the United States Constitution
The First Amendment to the United States Constitution is part of the Bill of Rights. The amendment prohibits the making of any law respecting an establishment of religion, impeding the free exercise of religion, abridging the freedom of speech, infringing on the freedom of the press, interfering...

right to free exercise of religion
Free Exercise Clause of the First Amendment
The Free Exercise Clause is the accompanying clause with the Establishment Clause of the First Amendment to the United States Constitution. The Establishment Clause and the Free Exercise Clause together read:...

.

The circle around a pentagram (transforming it in to a pentacle) is a symbol of "unity, wholeness, infinity, the goddess, and protection. To earth-centered religions throughout history as well as to many contemporary pagans, it represents the feminine spirit or force, the cosmos or a spiritualism Mother Earth, and a sacred space." The five-pointed star is representative of the four primal elements (earth, air, fire and water,) and traditionally a fifth, called spirit. The circle binds them together to create life. When pointing up, the pentagram can represent spirituality's dominance over the material (pentagram) bound inside the laws of the cosmos (circle). The upside-down facing pentagram, meanwhile, represents the physical world ruling over the spiritual, and has therefore been associated with dark magic. Other sources point to its origin in Chinese five-element philosophy (see feng shui
Feng shui
Feng shui ' is a Chinese system of geomancy believed to use the laws of both Heaven and Earth to help one improve life by receiving positive qi. The original designation for the discipline is Kan Yu ....

), as the natural balance between fire, water, earth, wood, and metal. This theory states that the direction it is pointing has nothing to do with good or evil, but rather the upside-down facing circle is for banishing. The circle is again for the concept the power within is bound by, this time for the circle of life.

### Satanism

Satanists use a pentagram with two points up, often inscribed in a double circle, with the head of a goat inside the pentagram. This is referred to as the Sigil of Baphomet
Sigil of Baphomet
The Sigil of Baphomet is the official insignium of the Church of Satan. It is also a symbol that is used by several other organizations, usually those associated with Satanism and the Left-Hand Path....

. They use it much the same way as the Pythagoreans, as Tartaros literally translates from Greek as a "Pit" or "Void" in Christian terminology (the word is used as such in the Bible, referring to the place where the fallen angel
Fallen angel
Fallen angel is a concept developed in Jewish mythology from interpretation of the Book of Enoch. The actual term fallen angel is not found in either the Hebrew Bible or the New Testament. Christians adopted the concept of fallen angels mainly based on their interpretations of the Book of...

s are fettered). The Pythagorean Greek letters are most often replaced by the Hebrew
Hebrew alphabet
The Hebrew alphabet , known variously by scholars as the Jewish script, square script, block script, or more historically, the Assyrian script, is used in the writing of the Hebrew language, as well as other Jewish languages, most notably Yiddish, Ladino, and Judeo-Arabic. There have been two...

letters לויתן forming the name Leviathan
Leviathan
Leviathan , is a sea monster referred to in the Bible. In Demonology, Leviathan is one of the seven princes of Hell and its gatekeeper . The word has become synonymous with any large sea monster or creature...

. Less esoteric LaVeyan Satanists
LaVeyan Satanism
LaVeyan Satanism, often referred to simply as Satanism among most adherents, was founded in 1966 by Anton LaVey. Its teachings are based on individualism, self-control and "eye for an eye" morality. Drawing influences from the rituals and ceremonies of occultist Aleister Crowley and the...

use it as a sign of rebellion or religious identification, the three downward points symbolising rejection of the holy Trinity
Trinity
The Christian doctrine of the Trinity defines God as three divine persons : the Father, the Son , and the Holy Spirit. The three persons are distinct yet coexist in unity, and are co-equal, co-eternal and consubstantial . Put another way, the three persons of the Trinity are of one being...

### Thelema

Aleister Crowley
Aleister Crowley
Aleister Crowley , born Edward Alexander Crowley, and also known as both Frater Perdurabo and The Great Beast, was an influential English occultist, astrologer, mystic and ceremonial magician, responsible for founding the religious philosophy of Thelema. He was also successful in various other...

also made use of the pentagram and in his Thelemic system of magick: an adverse or inverted pentagram represents the descent of spirit into matter, according to the interpretation of Lon Milo DuQuette
Lon Milo Duquette
Lon Milo DuQuette, AKA Rabbi Lamed Ben Clifford, is an American writer, lecturer, and occultist, best known as an author who applies humor in the field of Western Hermeticism.-Early life:...

. Crowley contradicted his old comrades in the Hermetic Order of the Golden Dawn
Hermetic Order of the Golden Dawn
The Hermetic Order of the Golden Dawn was a magical order active in Great Britain during the late 19th and early 20th centuries, which practiced theurgy and spiritual development...

, who following Levi considered this orientation of the symbol evil
Evil
Evil is the violation of, or intent to violate, some moral code. Evil is usually seen as the dualistic opposite of good. Definitions of evil vary along with analysis of its root motive causes, however general actions commonly considered evil include: conscious and deliberate wrongdoing,...

and associated it with the triumph of matter over spirit.

### Flags

While a solid five-pointed star
Five-pointed star
A five-pointed star is a very common ideogram throughout the world. If the colinear edges are joined together a pentagram is produced, which is the simplest of the unicursal star polygons, and a symbol of mystical and magical significance....

is found on many flags, the pentagram is relatively rare. It appears on two national flags, those of Ethiopia
Ethiopia
Ethiopia , officially known as the Federal Democratic Republic of Ethiopia, is a country located in the Horn of Africa. It is the second-most populous nation in Africa, with over 82 million inhabitants, and the tenth-largest by area, occupying 1,100,000 km2...

and Morocco
Morocco
Morocco , officially the Kingdom of Morocco , is a country located in North Africa. It has a population of more than 32 million and an area of 710,850 km², and also primarily administers the disputed region of the Western Sahara...

and in some coats of arms. According to Ivan Sache, on the Moroccan flags, the pentagram represents the link between God
God
God is the English name given to a singular being in theistic and deistic religions who is either the sole deity in monotheism, or a single deity in polytheism....

and the nation. It is also possible that both flags use the pentagram as a symbol of King Solomon (see Seal of Solomon
Seal of Solomon
In Medieval Jewish, Christian and Islamic legends, the Seal of Solomon was a magical signet ring said to have been possessed by King Solomon, which variously gave him the power to command demons, genies , or to speak with animals.-In legend :...

), the archetypal wise king of Jewish, Christian
Christian
A Christian is a person who adheres to Christianity, an Abrahamic, monotheistic religion based on the life and teachings of Jesus of Nazareth as recorded in the Canonical gospels and the letters of the New Testament...

and Muslim
Muslim
A Muslim, also spelled Moslem, is an adherent of Islam, a monotheistic, Abrahamic religion based on the Quran, which Muslims consider the verbatim word of God as revealed to prophet Muhammad. "Muslim" is the Arabic term for "submitter" .Muslims believe that God is one and incomparable...

lore, although the six-pointed Star of David
Star of David
The Star of David, known in Hebrew as the Shield of David or Magen David is a generally recognized symbol of Jewish identity and Judaism.Its shape is that of a hexagram, the compound of two equilateral triangles...

is a more common and more widely accepted symbol. In either case, the pentagram is a traditional symbol of both the Moroccan
Moroccan people
The Moroccan people are a people that share a common Moroccan culture, ancestry and speak the Moroccan variant of the Arabic language or a Berber language as a mother tongue....

and Ethiopian people
Ethiopian people
Ethiopian people or Ethnic Ethiopians are an ethnic group found in the horn of African country of Ethiopia.-Origins:Ethnic Ethiopians are one of the nearly 80 ethnic groups of the horn of Africa country and are found in every regional state of Ethiopia...

s, and, within Morocco, is also a symbol of the Alaouite dynasty
Alaouite Dynasty
The Alaouite Dynasty is the name of the current Moroccan royal family. The name Alaouite comes from the ‘Alī of its founder Moulay Ali Cherif who became Prince of Tafilalt in 1631. His son Mulay r-Rshid was able to unite and pacify the country...

.

## Other organizations

### Order of the Eastern Star

The Order of the Eastern Star
Order of the Eastern Star
The Order of the Eastern Star is a fraternal organization that both men and women can join. It was established in 1850 by Rob Morris, a lawyer and educator from Boston, Massachusetts, who had been an official with the Freemasons. It is based on teachings from the Bible, but is open to people of all...

, an organization associated with Freemasonry
Freemasonry
Freemasonry is a fraternal organisation that arose from obscure origins in the late 16th to early 17th century. Freemasonry now exists in various forms all over the world, with a membership estimated at around six million, including approximately 150,000 under the jurisdictions of the Grand Lodge...

, has employed a point-down pentagram as its symbol, with the five isosceles triangles of the points colored red, blue, yellow, white and green. This is an older form of the order's emblem and it is now more commonly depicted with the central pentagon rotated 36° so that it is no longer strictly a pentagram.

## In literature

In the medieval romance of Sir Gawain and the Green Knight
Sir Gawain and the Green Knight
Sir Gawain and the Green Knight is a late 14th-century Middle English alliterative romance outlining an adventure of Sir Gawain, a knight of King Arthur's Round Table. In the poem, Sir Gawain accepts a challenge from a mysterious warrior who is completely green, from his clothes and hair to his...

, the pentagram on Gawain
Gawain
Gawain is King Arthur's nephew and a Knight of the Round Table who appears very early in the Arthurian legend's development. He is one of a select number of Round Table members to be referred to as the greatest knight, most notably in Sir Gawain and the Green Knight...

's shield is given a Christian interpretation (see above).

In Goethe's Faust
Faust
Faust is the protagonist of a classic German legend; a highly successful scholar, but also dissatisfied with his life, and so makes a deal with the devil, exchanging his soul for unlimited knowledge and worldly pleasures. Faust's tale is the basis for many literary, artistic, cinematic, and musical...

, the pentagram prevents Mephistopheles
Mephistopheles
Mephistopheles is a demon featured in German folklore...

from leaving a room.
Mephistopheles:
I must confess, my stepping o'er
Thy threshold a slight hindrance doth impede;
The wizard-foot doth me retain.

Faust:
The pentagram thy peace doth mar?
To me, thou son of hell, explain,
How earnest thou in, if this thine exit bar?
Could such a spirit aught ensnare?

According to Eliphas Levi
Eliphas Levi
Eliphas Lévi, born Alphonse Louis Constant , was a French occult author and purported magician."Eliphas Lévi," the name under which he published his books, was his attempt to translate or transliterate his given names "Alphonse Louis" into Hebrew although he was not Jewish.His second wife was...

, the sign of the pentagram is exalted by Goethe in the monologue of Faust:
"... Ah, how do all my senses leap at this sight! I feel the young and sacred pleasure of life quivering in my nerves and veins. Was it a God who traced this sign which stills the vertigo of my soul, fills my poor heart with joy, and, in a mysterious rapture, unveils the forces of Nature around me? Am I myself a God? All is so clear to me: I behold in these simple line the revelation of active Nature to my soul. I realise for the first time the truth of the wise man's words: The world of spirits is not closed! Thy sense is obtuse, thy heart is dead! Arise! Bathe, O adept of science, thy breast, still enveloped by an unearthly veil, in the splendours of the dawning day!" (Faust, Part i.sc.i).

In H. P. Lovecraft
H. P. Lovecraft
Howard Phillips Lovecraft --often credited as H.P. Lovecraft — was an American author of horror, fantasy and science fiction, especially the subgenre known as weird fiction....

's Cthulhu Mythos
Cthulhu Mythos
The Cthulhu Mythos is a shared fictional universe, based on the work of American horror writer H. P. Lovecraft.The term was first coined by August Derleth, a contemporary correspondent of Lovecraft, who used the name of the creature Cthulhu - a central figure in Lovecraft literature and the focus...

stories, the version of The Elder Sign devised by August Derleth
August Derleth
August William Derleth was an American writer and anthologist. Though best remembered as the first publisher of the writings of H. P...

is a warped pentagram with a flaming eye or pillar of flame in the center. It was first described in Derleth's novel, The Lurker at the Threshold. (This was, however, different from the symbol that Lovecraft himself had envisaged.)

In T. S. Eliot
T. S. Eliot
Thomas Stearns "T. S." Eliot OM was a playwright, literary critic, and arguably the most important English-language poet of the 20th century. Although he was born an American he moved to the United Kingdom in 1914 and was naturalised as a British subject in 1927 at age 39.The poem that made his...

's The Dry Salvages
The Dry Salvages
"The Dry Salvages" is the third poem of T. S. Eliot's Four Quartets and marks the beginning of when the series was consciously being formed as a set of four poems. It was written and published in 1941 during the air-raids on Great Britain, an event that threatened him while giving lectures in the...

, reference to pentagrams is made in part V, verse 8:
By sortilege, or tea leaves, riddle the inevitable
With playing cards, fiddle with pentagrams
Or barbituric acids, or dissect
The recurrent image into pre-conscious terrors[...]

In Dan Brown
Dan Brown
Dan Brown is an American author of thriller fiction, best known for the 2003 bestselling novel, The Da Vinci Code. Brown's novels, which are treasure hunts set in a 24-hour time period, feature the recurring themes of cryptography, keys, symbols, codes, and conspiracy theories...

's novel The Da Vinci Code
The Da Vinci Code
The Da Vinci Code is a 2003 mystery-detective novel written by Dan Brown. It follows symbologist Robert Langdon and Sophie Neveu as they investigate a murder in Paris's Louvre Museum and discover a battle between the Priory of Sion and Opus Dei over the possibility of Jesus having been married to...

, the pentagram represents Venus, based on the successive inferior conjunctions of Venus against the Zodiac
Zodiac
In astronomy, the zodiac is a circle of twelve 30° divisions of celestial longitude which are centred upon the ecliptic: the apparent path of the Sun across the celestial sphere over the course of the year...

.

In Japanese culture
Culture of Japan
The culture of Japan has evolved greatly over the millennia, from the country's prehistoric Jōmon period to its contemporary hybrid culture, which combines influences from Asia, Europe and North America...

, the pentagram (五芒星 gobōsei) is a symbol of magical power, associated with the onmyoji Abe no Seimei
Abe no Seimei
was an onmyōji, a leading specialist of onmyōdō during the middle of the Heian Period in Japan. In addition to his prominence in history, he is a legendary figure in Japanese folklore and has been portrayed in a number of stories and films....

; it is a diagram of the "overcoming cycle" of the five Chinese elements. As a predominantly non-Christian country, with a different set of associations attached to the symbol, there is no social stigma associated with it.

## Geometry

The pentagram is the simplest regular
Regular polygon
A regular polygon is a polygon that is equiangular and equilateral . Regular polygons may be convex or star.-General properties:...

star polygon. The pentagram contains ten points (the five points of the star, and the five vertices of the inner pentagon) and fifteen line segments. It is represented by the Schläfli symbol {5/2}. Like a regular pentagon, and a regular pentagon with a pentagram constructed inside it, the regular pentagram has as its symmetry group
Symmetry group
The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...

the dihedral group
Dihedral group
In mathematics, a dihedral group is the group of symmetries of a regular polygon, including both rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry.See also: Dihedral symmetry in three...

of order 10.

### Construction

The pentagram can be constructed by connecting alternate vertices of a pentagon
Pentagon
In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The sum of the internal angles in a simple pentagon is 540°. A pentagram is an example of a self-intersecting pentagon.- Regular pentagons :In a regular pentagon, all sides are equal in length and...

; see details of the construction. It can also be constructed as a stellation
Stellation
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...

of a pentagon, by extending the edges of a pentagon until the lines intersect.

### Golden ratio

The golden ratio
Golden ratio
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989...

, φ = (1+√5)/2 ≈ 1.618, satisfying
plays an important role in regular pentagons and pentagrams. Each intersection of edges sections the edges in golden ratio: the ratio of the length of the edge to the longer segment is φ, as is the length of the longer segment to the shorter. Also, the ratio of the length of the shorter segment to the segment bounded by the 2 intersecting edges (a side of the pentagon in the pentagram's center) is φ. As the four-color illustration shows:

The pentagram includes ten isosceles triangles: five acute and five obtuse isosceles triangles. In all of them, the ratio of the longer side to the shorter side is φ. The acute triangles are golden triangles. The obtuse isosceles triangle highlighted via the colored lines in the illustration is a golden gnomon.

### Trigonometric values

See Exact trigonometric constants: Pentagon

As a result, in an isosceles triangle with one or two angles of 36°, the longer of the two side lengths is φ times that of the shorter of the two, both in the case of the acute as in the case of the obtuse triangle.

### Three-dimensional figures

See Uniform polyhedron: Icosahedral symmetry

Several polyhedra
Polyhedron
In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...

incorporate pentagrams:

### Higher dimensions

Orthogonal projections of higher dimensional polytopes can also create pentagrammic figures:
4D 5D

The regular 5-cell (4-simplex
Simplex
In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron,...

) has 5 vertices and 10 edges.

The rectified 5-cell
Rectified 5-cell
In four dimensional geometry, the rectified 5-cell is a uniform polychoron composed of 5 regular tetrahedral and 5 regular octahedral cells. Each edge has one tetrahedron and two octahedra. Each vertex has two tetrahedra and three octahedra. In total it has 30 triangle faces, 30 edges, and 10...

has 10 vertices and 30 edges.

The rectified 5-simplex has 15 vertices, seen in this orthogonal projection as 3 nested pentagrams.

The birectified 5-simplex has 20 vertices, seen in this orthogonal projection as 4 overlapping pentagrams.

All ten 4-dimensional Schläfli-Hess polychoron have either pentagrammic faces or vertex figure
Vertex figure
In geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...

elements.

## In Astronomy and nature

 Successive inferior conjunctions of Venus repeat very near a 13:8 orbital resonanceOrbital resonanceIn celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of... (The Earth orbits 8 times for every 13 orbits of Venus), creating a pentagrammic precession sequence.

## In visual arts

• The artist Martina Schettina
Martina Schettina
Martina Schettina is an Austrian artist.- Life :Martina Schettina was born in 1961 in the district Währing in Vienna. Her father was a Mathematician...

uses pentagrams in her paintings. The painting "Golden Pentagram" was shown at the Museumsquartier
Museumsquartier
The Museumsquartier is a 60,000 m² large area in the 7th district of the city of Vienna, Austria; it is the eighth largest cultural area in the world. The Museumsquartier contains Baroque buildings as well as Modern architecture by the architects Laurids and Manfred Ortner . The renovation of the...

in Vienna in 2010.
• Artist William Powhida
William Powhida
William Powhida is a visual artist and former art critic born in 1976 in New York. His work addresses the contemporary art industry.Topics have included creating an "enemies" list as well as letters addressed to contemporary curators , collectors and critics, requesting recognition...

employed pentagrams in his 2010 performance Surviving the Art World Using the Art of Sorcery at Hyperallergic in Brooklyn, NY. The artist performed curses that promised to "induce a favorable Friday New York Times review," "be paid within ninety days or three moons," "ward off annoying bloggers," or "beat your high estimate at auction."

The Pentagram was often a part of Motley Crue
Mötley Crüe
Mötley Crüe is an American heavy metal band formed in Los Angeles, California in 1981. The group was founded by bass guitarist Nikki Sixx and drummer Tommy Lee, who were later joined by lead guitarist Mick Mars and lead singer Vince Neil...

's early album covers and visual style.
• The metalcore band Oh, Sleeper
Oh, Sleeper
Oh, Sleeper is an American metalcore band from Fort Worth, Texas and is signed to Solid State Records. They have recorded three full-length albums to date, the most recent being their third album Children of Fire, released on September 6, 2011....

uses a "broken" pentagram with the top two triangles or "horns" missing, representing the downfall of Satan.

• Bahá'í symbols
Bahá'í symbols
Bahá'í symbols are symbols that have been used, or are used, to express identification with the Bahá'í Faith. While the five-pointed star is the symbol of the religion, being used to represent the human body and Messengers of God, more common symbols include the nine-pointed star, the Greatest...

• Command-at-Sea Pin
• Enneagram (geometry)
Enneagram (geometry)
In geometry, an enneagram is a nine-pointed geometric figure. It is sometimes called a nonagram.-Regular enneagram:A regular enneagram is constructed using the same points as the regular enneagon but connected in fixed steps...

• Heptagram
Heptagram
A heptagram or septegram is a seven-pointed star drawn with seven straight strokes.- Geometry :In general, a heptagram is any self-intersecting heptagon ....

• Hexagram
• List of regular polytopes#Two Dimensions 2
• List of symbols
• Mullet (heraldry)
Mullet (heraldry)
In heraldry, the term star may refer to any star-shaped charge with any number of rays, which may appear straight or wavy, and may or may not be pierced...

• Nonconvex uniform polyhedra with full icosahedral symmetry (many show a pattern of pentagrams)

• Pentachoron
Pentachoron
In geometry, the 5-cell is a four-dimensional object bounded by 5 tetrahedral cells. It is also known as the pentachoron, pentatope, or hyperpyramid...

- the 4-simplex
Simplex
In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimension. Specifically, an n-simplex is an n-dimensional polytope which is the convex hull of its n + 1 vertices. For example, a 2-simplex is a triangle, a 3-simplex is a tetrahedron,...

• Pentagram map
Pentagram map
In mathematics, the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane. The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections.Richard Schwartz...

(related concept)
• Pentalpha
Pentalpha
Pentalpha is a puzzle where the goal is to place nine stones on the ten intersections of a pentagram. The following rules need to be obeyed when placing the stones:#The stone has to visit two other points before reaching its final point....

• Petersen graph
Petersen graph
In the mathematical field of graph theory, the Petersen graph is an undirected graph with 10 vertices and 15 edges. It is a small graph that serves as a useful example and counterexample for many problems in graph theory. The Petersen graph is named for Julius Petersen, who in 1898 constructed it...

• Ptolemy's theorem
Ptolemy's theorem
In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral . The theorem is named after the Greek astronomer and mathematician Ptolemy...

• Red star
Red star
A red star, five-pointed and filled, is an important ideological and religious symbol which has been used for various purposes, such as: state emblems, flags, monuments, ornaments, and logos.- Symbol of communism :...

• Star (glyph)
Star (glyph)