A heptagram, septagram, septegram or septogram is a seven-point

star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...

drawn with seven straight strokes. The name ''heptagram'' combines a

numeral prefix Numeral or number prefixes are prefixes derived from Numeral (linguistics), numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous series of words. For example: * unicycle, bicycle, tricycle (1 ...

, ''

hepta- Numeral or number prefixes are prefixes derived from Numeral (linguistics), numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous series of words. For example: * unicycle, bicycle, tricycle (1 ...

'', with the

Greek Greek may refer to: Greece Anything of, from, or related to Greece, a country in Southern Europe: *Greeks, an ethnic group. *Greek language, a branch of the Indo-European language family. **Proto-Greek language, the assumed last common ancestor ...

suffix '' -gram''. The ''-gram'' suffix derives from ''γραμμῆ'' (''grammē'') meaning a line.

Geometry

In general, a heptagram is any self-intersecting

heptagon In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of ''septua-'', a Latin-derived numerical prefix, rather than ''hepta-'', a Greek-derived num ...

(7-sided

polygon In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed ''polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two toge ...

). There are two ''regular'' heptagrams, labeled as and , with the second number representing the vertex interval step from a regular

, . This is the smallest star polygon that can be drawn in two forms, as

irreducible fraction An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). ...

s. The two heptagrams are sometimes called the ''heptagram'' (for ) and the ''great heptagram'' (for ). The previous one, the regular

hexagram , can be seen as a compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green). A hexagram ( Greek language, Greek) or sexagram (Latin) is a six-pointed ...

, is a compound of two triangles. The smallest star polygon is the

pentagram A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle aroun ...

. The next one is the

octagram In geometry, an octagram is an eight-angled star polygon. The name ''octagram'' combine a Greek numeral prefix, '' octa-'', with the Greek suffix '' -gram''. The ''-gram'' suffix derives from γραμμή (''grammḗ'') meaning "line". Detai ...

and its related star figure (a compound of two squares), followed by the regular enneagram, which also has two forms: and , as well as one compound of three triangles .

Uses

Flags and heraldry

File:Coat of arms of Georgia (1918–1921; 1990–2004).svg, Former Georgian coat of arms, 1918–1921, 1991–2004 File:Roundel of Georgia.svg, Roundel of the

Georgian Air Force The Aviation and Air Defence Command of the Defense Forces of Georgia, Defence Forces ( ka, თავდაცვის ძალების ავიაციისა და საჰაერო თავდაცვის სარდლო ...

File:Eastern Band Cherokee Flag.svg, Flag of

Eastern Band Cherokee The Eastern Band of Cherokee Indians (EBCI), (Cherokee: ᏣᎳᎩᏱ ᏕᏣᏓᏂᎸᎩ, ''Tsalagiyi Detsadanilvgi'') is a federally recognized Indian Tribe based in Western North Carolina in the United States. They are descended from the smal ...

File:Flag of Occitania (with star).svg, The seven-pointed star of the Felibritge on the

Occitan Occitan may refer to: * Something of, from, or related to the Occitania territory in parts of France, Italy, Monaco and Spain. * Something of, from, or related to the Occitania administrative region of France. * Occitan language Occitan (; o ...

flag. File:Flag of Jordan.svg, The Jordanian flag, bearing the star that symbolizes

Al-Fatiha Al-Fatiha (alternatively transliterated Al-Fātiḥa or Al-Fātiḥah; ar, ألْفَاتِحَة, ; ), is the first ''surah'' (chapter) of the Quran. It consists of 7 '' ayah'' (verses) which are a prayer for guidance and mercy. Al-Fatiha i ...

File:Flag of Hokkaido Prefecture.svg, Symbol of

Hokkaido is Japan's second largest island and comprises the largest and northernmost prefecture, making up its own region. The Tsugaru Strait separates Hokkaidō from Honshu; the two islands are connected by the undersea railway Seikan Tunnel. The la ...

File:Emblem of Samarkand.svg, Coat of arms of

Samarkand fa, سمرقند , native_name_lang = , settlement_type = City , image_skyline = , image_caption = Clockwise from the top:Registan square, Shah-i-Zinda necropolis, Bibi-Khanym Mosque, view inside Shah-i-Zinda, ...

File:Commonwealth_Star.svg, Commonwealth Star as the crest of Coat of Arms of Australia * The seven-pointed star is incorporated into the flags of various bands of

Cherokee Indians The Cherokee (; chr, ᎠᏂᏴᏫᏯᎢ, translit=Aniyvwiyaʔi or Anigiduwagi, or chr, ᏣᎳᎩ, links=no, translit=Tsalagi) are one of the indigenous peoples of the Southeastern Woodlands of the United States. Prior to the 18th century, th ...

and the badges of

Navajo Nation Police The Navajo Nation Police (formerly known as the Navajo Tribal Police) is the law enforcement agency on the Navajo Nation in the Southwestern United States. It is under the Navajo Division of Public Safety. It is headed by a Chief of Police, si ...

(as well as other police). * The

Bennington flag Bennington is a town in Bennington County, Vermont, United States. It is one of two shire towns (county seats) of the county, the other being Manchester. As of the 2020 US Census, the population was 15,333. Bennington is the most populous to ...

, a historical American Flag, has thirteen seven-pointed stars along with the numerals "76" in the canton. * The

Flag of Jordan The flag of Jordan, officially adopted on 16 April 1928, is based on the 1916 flag of the Arab Revolt against the Ottoman Empire during World War I. The flag consists of horizontal black, white, and green bands that are connected by a red chevr ...

contains a seven-pointed star. * The

Flag of Australia The flag of Australia, also known as the Australian Blue Ensign, is based on the British Blue Ensign—a blue field with the Union Jack in the upper hoist quarter—augmented with a large white seven-pointed star (the Commonwealth Star) and a ...

employs five heptagrams and one

to depict the

Southern Cross Crux () is a constellation of the southern sky that is centred on four bright stars in a cross-shaped asterism commonly known as the Southern Cross. It lies on the southern end of the Milky Way's visible band. The name ''Crux'' is Latin for ...

constellation and the

Commonwealth Star The Commonwealth Star (also known as the Federation Star, the Seven Point Star, or the Star of Federation) is a seven-pointed star symbolising the Federation of Australia which came into force on 1 January 1901. Six points of the Star represent ...

. * Some old versions of the

coat of arms of Georgia (country) The coat of arms of Georgia is one of the national symbols of the republic. It is partially based on the medieval arms of the Georgian royal house and features Saint George, the traditional patron saint of Georgia. In addition to St. George, t ...

including the

Georgian Soviet Socialist Republic The Georgian Soviet Socialist Republic (Georgian SSR; ka, საქართველოს საბჭოთა სოციალისტური რესპუბლიკა, tr; russian: Грузинская Советская Соц� ...

used the heptagram as an element. * A seven-pointed star is used as the

badge A badge is a device or accessory, often containing the insignia of an organization, which is presented or displayed to indicate some feat of service, a special accomplishment, a symbol of authority granted by taking an oath (e.g., police and fi ...

in many sheriff's departments and some smaller-community police departments. *A seven-pointed star is used in the

otherkin Otherkin are a subculture of people who identify as not entirely human. Some otherkin believe their identity derives from reincarnation, a non-human soul, ancestry, symbolism, or metaphor. Others attribute it to unusual psychology and do not h ...

pride flag.

Law enforcement

File:Seal of the California Highway Patrol.svg, Seal of the :California Highway Patrol

Religious and occult symbolism

* The heptagram became a traditional symbol for warding off evil in Catholicism. * The symbol is also used in Kabbalist Judaism. * In

Islam Islam (; ar, ۘالِإسلَام, , ) is an Abrahamic religions, Abrahamic Monotheism#Islam, monotheistic religion centred primarily around the Quran, a religious text considered by Muslims to be the direct word of God in Islam, God (or ...

, the heptagram is used to represent the first seven verses in the

Quran The Quran (, ; Standard Arabic: , Classical Arabic, Quranic Arabic: , , 'the recitation'), also romanized Qur'an or Koran, is the central religious text of Islam, believed by Muslims to be a revelation in Islam, revelation from God in Islam, ...

. * The heptagram is used in the symbol for

Babalon Babalon (also known as the Scarlet Woman, Great Mother or Mother of Abominations) is a goddess found in the occult system of Thelema, which was established in 1904 with the writing of ''The Book of the Law'' by English author and occultist Al ...

in Aleister Crowley's occult system

Thelema Thelema () is a Western esoteric and occult social or spiritual philosophy and new religious movement founded in the early 1900s by Aleister Crowley (1875–1947), an English writer, mystic, occultist, and ceremonial magician. The word '' ...

. * The heptagram is known among

neopagan Modern paganism, also known as contemporary paganism and neopaganism, is a term for a religion or family of religions influenced by the various historical pre-Christian beliefs of pre-modern peoples in Europe and adjacent areas of North Afric ...

s as the ''Elven Star'' or ''Fairy Star''. It is treated as a sacred symbol in various modern pagan and witchcraft traditions.

Blue Star Wicca Blue Star Wicca is one of a number of Wiccan traditions, and was created in the United States in the 1970s based loosely on the Gardnerian and Alexandrian traditions. It continues to be practiced today in areas of the United States (including ...

also uses the symbol, where it is referred to as a ''septegram''. The second heptagram is a symbol of magical power in some

pagan Paganism (from classical Latin ''pāgānus'' "rural", "rustic", later "civilian") is a term first used in the fourth century by early Christians for people in the Roman Empire who practiced polytheism, or ethnic religions other than Judaism. ...

spiritualities. * In

alchemy Alchemy (from Arabic: ''al-kīmiyā''; from Ancient Greek: χυμεία, ''khumeía'') is an ancient branch of natural philosophy, a philosophical and protoscientific tradition that was historically practiced in China, India, the Muslim world, ...

, a seven-sided star can refer to the seven planets which were known to early alchemists, and also, the seven alchemical substances: fire, water, air, earth, sulphur, salt and mercury. * In Polynesia, the seven-pointed star is used often in imagery, basket making, tattoos, and is considered to be a symbol of Kanaloa, the first Polynesian navigator. * The seven-sided star is an important symbol of the Cherokee people of southern Appalachia, representing the seven clans of the Cherokee and the sacred number seven.

In popular culture

* The logo of American shoe brand

DC Shoes DC Shoes is an American company that specializes in footwear for action sports, including skateboarding and snowboarding. The company also manufactures apparel, bags, accessories, hats, tshirts, and posters. History The company was founded in ...

features a 7/3 heptagram in the letter C. * The seven-pointed star is used as the logo for the international Danish shipping company A.P. Moller–Maersk Group, sometimes known simply as

Maersk (), also known simply as Maersk (), is a Danish shipping company, active in ocean and inland freight transportation and associated services, such as supply chain management and port operation. Maersk was the largest container shipping line a ...

. * In

George R. R. Martin George Raymond Richard Martin (born George Raymond Martin; September 20, 1948), also known as GRRM, is an American novelist, screenwriter, television producer and short story writer. He is the author of the series of epic fantasy novels ''A Song ...

's novel series ''

A Song of Ice and Fire ''A Song of Ice and Fire'' is a series of epic fantasy novels by the American novelist and screenwriter George R. R. Martin. He began the first volume of the series, ''A Game of Thrones'', in 1991, and it was published in 1996. Martin, who init ...

'' and its TV version

Game of Thrones ''Game of Thrones'' is an American fantasy drama television series created by David Benioff and D. B. Weiss for HBO. It is an adaptation of ''A Song of Ice and Fire'', a series of fantasy novels by George R. R. Martin, the first ...

, a seven-pointed star serves as the symbol of the Faith of the Seven. * In the manga series MeruPuri, a magical mirror/ portal is in the shape of a heptagram. The symbol is also seen during spellcasting. * Finnish rock band HIM used a heptagram on the cover of their eighth studio album

Tears on Tape ''Tears on Tape'' is the eighth and final studio album by Finnish rock band HIM, released 26 April 2013 in Finland, 29 April 2013 in Europe, and on 30 April 2013 in the US and Canada. Background At the beginning of 2011 HIM parted ways with ...

. * American heavy metal band Darkest Hour used a heptagram on the cover of their eighth studio album Darkest Hour. * English Singer

Damon Albarn Damon Albarn (; born 23 March 1968) is an English-Icelandic musician, singer-songwriter and composer, best known as the frontman and primary lyricist of the rock band Blur and as the co-creator and primary musical contributor of the virtual ...

uses a heptagram as a symbol in his solo performances. * The heptagram is used by some members of the

subculture as an identifier. * The American Progressive Rock Metal Band “

Tool A tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates ba ...

” uses an ‘open’ seven pointed symbol for their fan group, The Tool Army. It is ‘open’ to signify an invitation into the collective unconscious. *The American Pop Rock musician William Sunshine used a heptagram as the album art for his first EP A Demonstrative Manifesto.

References

Bibliography * Grünbaum, B. and G.C. Shephard; ''Tilings and Patterns'', New York: W. H. Freeman & Co., (1987), . * Grünbaum, B.; Polyhedra with Hollow Faces, ''Proc of NATO-ASI Conference on Polytopes ... etc. (Toronto 1993)'', ed T. Bisztriczky et al., Kluwer Academic (1994) pp. 43–70. *

John H. Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English people, English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to ...

, Heidi Burgiel, Chaim Goodman-Strass, ''The Symmetries of Things'' 2008, (Chapter 26. pp. 404: Regular star-polytopes Dimension 2)

External links

*
Approximate construction method
{{Polygons 07 7 (number)