A hexagram (Greek) or sexagram (Latin) is a six-pointed geometric star figure with the Schläfli symbol {6/2}, 2{3}, or {{3}}. Since there are no true regular continuous hexagrams, the term is instead used to refer to a compound figure of two equilateral triangles. The intersection is a regular hexagon.
The hexagram is part of an infinite series of shapes which are compounds of two n-dimensional simplices. In three dimensions, the analogous compound is the stellated octahedron, and in four dimensions the compound of two 5-cells is obtained.
It has been historically used in various religious and cultural contexts and as decorative motifs. The symbol was used as a decorative motif in medieval Christian churches and Jewish synagogues. The hexagram is thought to have originated in Buddhism and was also used by Hindus. It was used by Muslims as a mystic symbol in the medieval period, known as the Seal of Solomon, depicted as either a hexagram or pentagram. [3]
Group theory
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In mathematics, the root system for the simple Lie group G2 is in the form of a hexagram, with six long roots and six short roots.
Construction by compass and a straight edge
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A six-pointed star, like a regular hexagon, can be created using a compass and a straight edge:
Construction by linear algebra
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A regular hexagram can be constructed by orthographically projecting any cube onto a plane through three vertices that are all adjacent to the same vertex. The twelve midpoints to edges of the cube form a hexagram. For example, consider the projection of the unit cube with vertices at the eight possible binary vectors in three dimensions ( 1 , 0 , 0 ) , ( 0 , 1 , 0 ) , ( 0 , 0 , 1 ) , ( 1 , 1 , 0 ) , ( 1 , 0 , 1 ) , ( 0 , 1 , 1 ) , ( 1 , 1 , 1 ) {\displaystyle (1,0,0),(0,1,0),(0,0,1),(1,1,0),(1,0,1),(0,1,1),(1,1,1)} onto the plane x + y + z = 1 {\displaystyle x+y+z=1} . The midpoints are ( 0 , 0 , 1 / 2 ) , ( 0 , 1 / 2 , 1 / 2 ) , ( 0 , 1 , 1 / 2 ) , ( 1 , 1 , 1 / 2 ) {\displaystyle (0,0,1/2),(0,1/2,1/2),(0,1,1/2),(1,1,1/2)} , and all points resulting from these by applying a permutation to their entries. These 12 points project to a hexagram: six vertices around the outer hexagon and six on the inner.
Origins and shape
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As a derivative of two overlapping triangles, the hexagram may have developed from different peoples with no direct correlation to one another.
The mandala symbol called yantra, found on ancient South Indian Hindu temples, is a geometric toolset that incorporates hexagrams into its framework. It symbolizes the nara-narayana, or perfect meditative state of balance achieved between Man and God, and if maintained, results in "moksha," or "nirvana" (release from the bounds of the earthly world and its material trappings).[citation needed]
Some researchers have theorized that the hexagram represents the astrological chart at the time of David's birth or anointment as king. The hexagram is also known as the "King's Star" in astrological circles.[citation needed]
In antique papyri, pentagrams, together with stars and other signs, are frequently found on amulets bearing the Jewish names of God, and used to guard against fever and other diseases. Curiously the hexagram is not found among these signs. In the Greek Magical Papyri[citation needed] (Wessely, l.c. pp. 31, 112) at Paris and London there are 22 signs side by side, and a circle with twelve signs, but neither a pentagram nor a hexagram.[citation needed]
Religious usage
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Indian religions
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Diagram showing the two mystic syllables Om and HrimSix-pointed stars have also been found in cosmological diagrams in Hinduism, Buddhism, and Jainism. The reasons behind this symbol's common appearance in Indic religions and the West are unknown. One possibility is that they have a common origin. The other possibility is that artists and religious people from several cultures independently created the hexagram shape, which is a relatively simple geometric design.
Within Indic lore, the shape is generally understood to consist of two triangles—one pointed up and the other down—locked in harmonious embrace. The two components are called "Om" and the "Hrim" in Sanskrit, and symbolize man's position between earth and sky. The downward triangle symbolizes Shakti, the sacred embodiment of femininity, and the upward triangle symbolizes Shiva, or Agni Tattva, representing the focused aspects of masculinity. The mystical union of the two triangles represents Creation, occurring through the divine union of male and female. The two locked triangles are also known as 'Shanmukha'—the six-faced, representing the six faces of Shiva & Shakti's progeny Kartikeya. This symbol is also a part of several yantras and has deep significance in Hindu ritual worship and history.
Anahata: The Heart ChakraIn Buddhism, some old versions of the Bardo Thodol, also known as The "Tibetan Book of the Dead", contain a hexagram with a swastika inside. It was made up by the publishers for this particular publication. In Tibetan, it is called the "origin of phenomenon" (chos-kyi 'byung-gnas). It is especially connected with Vajrayogini, and forms the center part of her mandala. In reality, it is in three dimensions, not two, although it may be portrayed either way.
The Shatkona is a symbol used in Hindu yantra that represents the union of both the male and feminine form. More specifically it is supposed to represent Purusha (the supreme being), and Prakriti (mother nature, or causal matter). Often this is represented as Shiva – Shakti.[4]
Anahata or heart chakra is the fourth primary chakra, according to Hindu Yogic, Shakta and Buddhist Tantric traditions. In Sanskrit, anahata means "unhurt, unstruck, and unbeaten". Anahata Nad refers to the Vedic concept of unstruck sound (the sound of the celestial realm). Anahata is associated with balance, calmness, and serenity.
Judaism
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The Star of David in the oldest surviving complete copy of the Masoretic text, the Leningrad Codex, dated 1008.The Magen David is a generally recognized symbol of Judaism and Jewish identity and is also known colloquially as the Jewish Star or "Star of David." Its usage as a sign of Jewish identity began in the Middle Ages, though its religious usage began earlier, with the current earliest archeological evidence being a stone bearing the shield from the arch of a 3–4th century synagogue in the Galilee.[5]
Christianity
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The first and the most important Armenian Cathedral of Etchmiadzin (303 AD, built by the founder of Christianity in Armenia) is decorated with many types of ornamented hexagrams and so is the tomb of an Armenian prince of the Hasan-Jalalyan dynasty of Khachen (1214 AD) in the Gandzasar Church of Artsakh.
The hexagram may be found in some Churches and stained-glass windows. In Christianity, it is sometimes called the star of creation. A very early example, noted by Nikolaus Pevsner, can be found in Winchester Cathedral, England in one of the canopies of the choir stalls, circa 1308.[6]
Latter-day Saints (Mormons)
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Star of David on the Salt Lake Assembly HallThe Star of David is also used less prominently by the Church of Jesus Christ of Latter-day Saints, in the temples and in architecture. It symbolizes God reaching down to man and man reaching up to God, the union of Heaven and earth. It may also symbolize the Tribes of Israel and friendship and their affinity towards the Jewish people. Additionally, it is sometimes used to symbolize the quorum of the twelve apostles, as in Revelation 12, wherein the Church of God is symbolized by a woman wearing a crown of twelve stars. It is also sometimes used to symbolize the Big Dipper, which points to the North Star, a symbol of Jesus Christ.
Islam
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The symbol is known in Arabic as Khātem Sulaymān (Seal of Solomon; خاتم سليمان) or Najmat Dāwūd (Star of David; نجمة داوود). The "Seal of Solomon" may also be represented by a five-pointed star or pentagram.
In the Qur'an, it is written that David and King Solomon (Arabic, Suliman or Sulayman) were prophets and kings, and are figures revered by Muslims. The Medieval pre-Ottoman Hanafi Anatolian beyliks of the Karamanids and Jandarids used the star on their flag.[7] The symbol also used on Hayreddin Barbarossa flag. Today the six-pointed star can be found in mosques and on other Arabic and Islamic artifacts.
Usage in heraldry
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In heraldry and vexillology, a hexagram is a fairly common charge employed, though it is rarely called by this name. In Germanic regions it is known simply as a "star." In English and French heraldry, however, the hexagram is known as a "mullet of six points," where mullet is a French term for a spur rowel which is shown with five pointed arms by default unless otherwise specified. In Albanian heraldry and vexillology, hexagram has been used since classical antiquity and it is commonly referred to as sixagram. The coat of arms of the House of Kastrioti depicts the hexagram on a pile argent over the double headed eagle.
Usage in Theosophy
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The Star of David is used in the seal and the emblem of the Theosophical Society (founded in 1875). Although it is more pronounced, it is used along with other religious symbols. These include the Swastika, the Ankh, the Aum, and the Ouroboros. The star of David is also known as the Seal of Solomon, which was its original name, being in regular use until around 50 years ago.
Usage in occultism
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The hexagram, like the pentagram, was and is used in practices of the occult and ceremonial magic and is attributed to the 7 "old" planets outlined in astrology.
The six-pointed star is commonly used both as a talisman[8] and for conjuring spirits and spiritual forces in diverse forms of occult magic. In the book The History and Practice of Magic, Vol. 2, the six-pointed star is called the talisman of Saturn and it is also referred to as the Seal of Solomon.[9] Details are given in this book on how to make these symbols and the materials to use.
Double hexagramTraditionally, the Hexagram can be seen as the combination of the four elements. Fire is symbolized as an upwards pointing triangle, while Air (its elemental opposite) is also an upwards pointing triangle, but with a horizontal line through its center. Water is symbolized as a downwards pointing triangle, while Earth (its elemental opposite) is also a downwards pointing triangle, but with a horizontal line through its center. When combined swith the symbols of fire and water, a hexagram (six-pointed star) is created. The same follows when combining the symbols of air and earth. Both hexagrams combined are called a double-hexagram. Thus, a combination of the elements is created.[10]
In Rosicrucian and Hermetic Magic, the seven Traditional planets correspond with the angles and the center of the Hexagram as follows, in the same patterns as they appear on the Sephiroth and on the Tree of Life. Saturn, although formally attributed to the Sephira of Binah, within this frame work nonetheless occupies the position of Daath.[11]
In alchemy, the two triangles represent the reconciliation of the opposites of fire and water.[12]
The hexagram is used as a sign for quintessence, the fifth element.[citation needed]
Usage in Freemasonry
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"The interlacing triangles or deltas symbolize the union of the two principles or forces, the active and passive, male and female, pervading the universe ... The two triangles, one white and the other black, interlacing, typify the mingling of apparent opposites in nature, darkness and light, error and truth, ignorance and wisdom, evil and good, throughout human life." – Albert G. Mackey: Encyclopedia of Freemasonry[page needed][failed verification]
The hexagram is featured within and on the outside of many Masonic temples as a decoration. It may have been[according to whom?] found within the structures of King Solomon's temple, from which Freemasons are inspired in their philosophies and studies. Like many other symbols in Freemasonry, the deciphering of the hexagram is non-dogmatic and left to the interpretation of the individual.[citation needed]
Other uses
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Ulster Banner Aerial photograph of Heathrow Airport, London, 1955 A hexagram appears on the Dardania Flag, proposed for Kosovo by the Democratic League of Kosovo.The Raëlian symbol with the swastika (left) and the alternative spiral version (right)
Worthing railway station platform 2 canopyFlags
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Other symbolic uses
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citation needed
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Unicode
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Other hexagrams
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The figure {6/3} can be shown as a compound of three digons.
Other hexagrams can be constructed as a continuous path.
Regular compounds D2 symmetrySee also
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References
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The Seal of Solomon or Ring of Solomon (Hebrew: חותם שלמה, Ḥotam Shlomo; Arabic: خاتم سليمان, Khātam Sulaymān; Turkish: Mühr-ü Süleyman) is the legendary signet ring attributed to the Israelite king Solomon in medieval mystical traditions, from which it developed in parallel within Jewish mysticism, Islamic mysticism and Western occultism.
It is often depicted in the shape of either a pentagram or a hexagram. In mystic Islamic and Jewish lore, the ring is variously described as having given Solomon the power to command the supernatural, including shedim and jinn, and also the ability to speak with animals. Due to the proverbial wisdom of Solomon, it came to be seen as an amulet or talisman, or a symbol or character in medieval magic and Renaissance magic, occultism, and alchemy.
The seal is the predecessor to the Star of David, a Jewish symbol, and in modern vexillology, it features on the Flag of Israel. The pentagram on the Flag of Morocco also represents the seal.[1] The Seal of Solomon was also depicted on the flag of Nigeria during British colonial rule.[2]
History
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Silver coin minted in the name of Eretna in 1351 CE in Erzincan, Turkey. It includes an inscription in the Uyghur script that reads sultan adil. A hexagram on the obverse of a Moroccan 4 Falus coin, dated AH 1290 (AD 1873/4). A variant form of the "Secret Seal of Solomon", as seen in the 17th-century grimoire The Lesser Key of Solomon.The earliest references to Solomon's seal or signet stem from within Jewish traditions. It is first mentioned by the first-century Jewish historian Josephus,[4](8.41-49) and is similarly referenced by the third-century Jewish magical text Sefer HaRazim,[5] and an aggadic section of the Tractate Gittin within the Babylonian Talmud as well.[6] In parallel, a first century Greek manual of Judeo-Christian magic known as Testament of Solomon also makes reference to the Seal of Solomon.
The tradition of Solomon's Seal later made its way into Islamic Arab sources, as Gershom Scholem (the founder of the modern, academic study of Kabbalah) attests "It is difficult to say for how long certain definite names have been used for several of the most common seals. The Arabs made many such terms especially popular, but just the names Seal of Solomon and Shield of David, which are often used interchangeably for the two emblems, go back to pre-Islamic Jewish magic. They did not originate among the Arabs who, incidentally, know only the designation Seal of Solomon."[7]
The legend of the Seal of Solomon was developed primarily by medieval Middle Eastern writers, who related that the ring was engraved by God and was given to the king directly from heaven. The ring was made from brass and iron, and the two parts were used to seal written commands to good and evil spirits, respectively. In one tale, a demon — either Asmodeus or Sakhr — obtained possession of the ring and ruled in Solomon's stead for forty days. In a variant of the tale of the ring of Polycrates from Herodotus, the demon eventually threw the ring into the sea, where it was swallowed by a fish, caught by a charitable fisherman, who unknowingly fed it to the displaced Solomon, restoring him to power.[8][a]
The date of origin legends surrounding the Seal of Solomon is difficult to establish. A legend of a magic ring with which the possessor could command demons was already current in the 1st century (Josephus[4](8.2) telling of one Eleazar who used such a ring in the presence of Vespasian), but the association of the name of Solomon with such a ring is likely medieval notwithstanding the 2nd century apocryphal text the Testament of Solomon. The Tractate Gittin (fol. 68) of the Talmud has a story involving Solomon, Asmodeus, and a ring with the divine name engraved: Solomon gives the ring and a chain to one Benaiahu son of Jehoiada to catch the demon Ashmedai, to obtain the demon's help to build the temple; Ashmedai later tricks Solomon into giving him the ring and swallows it.[b]
The specification of the design of the seal as a hexagram seems to arise from a medieval Arab tradition, and most scholars assume that the symbol entered the Kabbalistic tradition of medieval Spain from Arabic literature.[11] The representation as a pentagram, by contrast, seems to arise in the Western tradition of Renaissance magic (which was in turn strongly influenced by medieval Arab and Jewish occultism); W. Kennett (1660–1728) makes reference to a "pentangle of Solomon" with the power of exorcising demons.[12]
Hexagrams feature prominently in Jewish esoteric literature from the early medieval period, and it has been hypothesized that the tradition of Solomon's Seal may possibly predate Islam and date to early Rabbinical esoteric tradition, or to early alchemy in Hellenistic Judaism in 3rd century Egypt.[13]
The seal appears profusely in the decoration of the 17th-century Catholic Sacromonte Abbey, in Granada, Spain, as a symbol of wisdom.[14] The Seal of Solomon was also discovered in Palestine during the Ottoman period, when it was etched in stone above windows and doors and on Muslim tombs. A few examples were found in houses in Saris and on graves in Jaffa.[15]
An "Order of Solomon's Seal" was established in 1874 in Ethiopia, where the ruling house claimed descent from Solomon.[16]
Other traditions
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In Islamic eschatology, some believe that the Beast of the Earth, which should appear near the Last Judgment day, will come bearing "the Seal of Solomon", and will use the latter to stamp the noses of the unbelievers.[17]
Use in vexillology
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In 1354, King of Bohemia Charles IV prescribed for the Jews of Prague a red flag with both David's shield and Solomon's seal, while the red flag with which the Jews met King Matthias of Hungary in the 15th century showed two pentagrams with two golden stars.[18]
The pentagram on the current flag of Morocco is meant to represent the Seal,[1] as well as the five pillars of Islam.[19]
The hexagram or Star of David, which became a symbol of Judaism in the modern period and was placed on the flag of Israel in 1948, has its origins in 14th-century depictions of the Seal of Solomon.
In popular culture
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Lippmann Moses Büschenthal (d. 1818) wrote a tragedy with the title Der Siegelring Salomonis ("the signet-ring of Solomon").
Memes have been circulated online that use the seal to portray the digital world, computers and the internet as inhabited by ''jinn'' (demons).[20]
"Solomon is represented as having authority over spirits, animals, wind, and water, all of which obeyed his orders by virtue of a magic ring set with the four jewels given him by the angels that had power over these four realms. [...] It was Solomon's custom to take off the ring when he was about to wash, and to give it to one of his wives, Amina, to hold.On one occasion, when the ring was in Amina's keeping, the rebellious spirit Sakhr took on Solomon's form and obtained the ring. He then seated himself on the throne and ruled for forty days, during which time the real king wandered about the country, poor and forlorn. On the fortieth day, Sakhr dropped the ring into the sea; there it was swallowed by a fish, which was caught by a poor fisherman and given to Solomon for his supper. Solomon cut open the fish, found the ring, and returned to power. His forty days' exile had been sent in punishment for the idolatry practiced in his house for forty days, although unknown to him, by one of his wives".
"Solomon thereupon sent thither Benaiahu son of Jehoiada, giving him a chain on which was graven the [Divine] Name and a ring on which was graven the Name and fleeces of wool and bottles of wine.Benaiahu went and dug a pit lower down the hill, and let the water flow into it[13] and stopped [the hollow] with the fleeces of wool, and he then dug a pit higher up and poured the wine into it[14] and then filled up the pits. He then went and sat on a tree.When Ashmedai came he examined the seal, then opened the pit and found it full of wine. He said, 'it is written,,[15] and it is also written,.[16] I will not drink it.' Growing thirsty, however, he could not resist, and he drank till he became drunk, and fell asleep. Benaiahu then came down and threw the chain over him and fastened it. When he awoke he began to struggle, whereupon he [Benaiahu] said,. [...]Solomon kept him [Ashmedai] with him until he had built the Temple. One day when he was alone with him, he said, 'it is written,' ["the strength of a wild ox"], 'and we explain thatmeans the ministering angels andmeans the demons. What is your superiority over us?' He said to him, 'Take the chain off me and give me your ring, and I will show you.' So he took the chain off him and gave him the ring. He then swallowed him, [viz. "it": the ring] and placing one wing on the earth and one on the sky he hurled him four hundred parasangs.In reference to that incident, Solomon said,
See also
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References
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