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

star A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...

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

numeral prefix Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous series of words. For example: *triangle, quadrilateral, pentagon, hexagon, octagon ...

, ''

hepta- Numeral or number prefixes are prefixes derived from numerals or occasionally other numbers. In English and many other languages, they are used to coin numerous series of words. For example: *triangle, quadrilateral, pentagon, hexagon, octagon ...

'', with the

Greek Greek may refer to: 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 of all kno ...

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 ''Wikt:septa-, septa-'' (an elision of ''Wikt:septua-, septua-''), a Latin-derived numerical prefix, rather than ...

(7-sided

polygon In geometry, a polygon () is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its '' edges'' or ''sides''. The points where two edges meet are the polygon ...

). 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 polygon, 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 l ...

, 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 around ...

. The next one is the

octagram In geometry, an octagram is an eight-angled star polygon. The name ''octagram'' combine a Greek numeral prefix, ''wikt:octa-, octa-'', with the Greek language, Greek suffix ''wikt:-gram, -gram''. The ''-gram'' suffix derives from γραμμή ...

and its related star figure (a compound of two squares), followed by the regular

enneagram Enneagram may refer to: * Enneagram (geometry), a nine-sided star polygon with various configurations * Enneagram of Personality, a model of human personality illustrated by an enneagram figure See also * Enneagon In geometry, a nonagon () or ...

, 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: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, spoken in parts o ...

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

Al-Fatiha Al-Fatiha () is the first chapter () of the Quran. It consists of seven verses (') which consist of a prayer for guidance and mercy. Al-Fatiha is recited in Muslim obligatory and voluntary prayers, known as ''salah''. The primary literal mea ...

File:Flag of Hokkaido Prefecture.svg, Symbol of

Hokkaido is the list of islands of Japan by area, second-largest island of Japan and comprises the largest and northernmost prefectures of Japan, prefecture, making up its own list of regions of Japan, region. The Tsugaru Strait separates Hokkaidō fr ...

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

Samarkand Samarkand ( ; Uzbek language, Uzbek and Tajik language, Tajik: Самарқанд / Samarqand, ) is a city in southeastern Uzbekistan and among the List of oldest continuously inhabited cities, oldest continuously inhabited cities in Central As ...

File:Commonwealth_Star.svg, Commonwealth Star as the crest of

Coat of Arms of Australia The coat of arms of Australia, officially the Commonwealth Coat of Arms, is a formal symbol of the Commonwealth of Australia. It depicts a shield, containing symbols of Australia's six states, and is held up by native Australian animals, the ka ...

File:Flag of Cook County, Illinois.svg, The flag of

Cook County Cook County is the most populous county in the U.S. state of Illinois and the second-most-populous county in the United States, after Los Angeles County, California. More than 40 percent of all residents of Illinois live within Cook County. ...

Illinois Illinois ( ) is a U.S. state, state in the Midwestern United States, Midwestern United States. It borders on Lake Michigan to its northeast, the Mississippi River to its west, and the Wabash River, Wabash and Ohio River, Ohio rivers to its ...

, adopted in June 2022 and taking design cues from the Flag of

Chicago Chicago is the List of municipalities in Illinois, most populous city in the U.S. state of Illinois and in the Midwestern United States. With a population of 2,746,388, as of the 2020 United States census, 2020 census, it is the List of Unite ...

, its

county seat A county seat is an administrative center, seat of government, or capital city of a county or parish (administrative division), civil parish. The term is in use in five countries: Canada, China, Hungary, Romania, and the United States. An equiva ...

File:CHE_Thun_Flag.svg, The coat of arms and flag of

Thun Thun () is a List of towns in Switzerland, town and a Municipalities of Switzerland, municipality in the administrative district of Thun (administrative district), Thun in the Cantons of Switzerland, canton of Canton of Bern, Bern in Switzerland. ...

Switzerland * The seven-pointed star is incorporated into the flags of various bands of

Cherokee Indians The Cherokee (; , or ) people are one of the Indigenous peoples of the Southeastern Woodlands of the United States. Prior to the 18th century, they were concentrated in their homelands, in towns along river valleys of what is now southwestern ...

and the badges of Navajo Nation Police (as well as other police). * The Bennington flag, 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 Flag ...

contains a seven-pointed star. * The

Flag of Australia The national flag of Australia 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 representation of the Crux, Southe ...

employs five heptagrams and one

to depict the

Southern Cross CRUX is a lightweight x86-64 Linux distribution targeted at experienced Linux users and delivered by a tar.gz-based package system with BSD-style initscripts. It is not based on any other Linux distribution. It also utilizes a ports system to ...

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, originally as a six-pointed star ...

. * Some old versions of the coat of arms of Georgia including the

Georgian Soviet Socialist Republic The Georgian Soviet Socialist Republic, also known as Soviet Georgia, the Georgian SSR, or simply Georgia, was one of the republics of the Soviet Union from its second occupation (by the Red Army) in 1921 to its independence in 1991. Cotermin ...

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 fir ...

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

otherkin Otherkin is a subculture of people who identify as partially or entirely nonhuman. Some otherkin believe their identity derives from non-physical spiritual phenomena, such as having a nonhuman soul or reincarnation. Some otherkin give non-spi ...

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. * 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 A ...

in Aleister Crowley's occult system

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

. * The heptagram is known among

neopagan Modern paganism, also known as contemporary paganism and neopaganism, spans a range of new religious movements variously influenced by the beliefs of pre-modern peoples across Europe, North Africa, and the Near East. Despite some common simila ...

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. Origins and history The "Coven of the Blue Star" and the traditions was es ...

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 (, 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 Christianity, Judaism, and Samaritanism. In the time of the ...

spiritualities. * In

alchemy Alchemy (from the Arabic word , ) is an ancient branch of natural philosophy, a philosophical and protoscientific tradition that was historically practised in China, India, the Muslim world, and Europe. In its Western form, alchemy is first ...

, 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

astrology Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that propose that information about human affairs and terrestrial events may be discerned by studying the apparent positions ...

. For example, the planetary hours, from which comes the

names of the days of the week In a vast number of languages, the names given to the seven days of the week are derived from the names of the classical planets in Hellenistic astronomy, which were in turn named after contemporary deities, a system introduced by the Sumer ...

. * 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, Inc. is an American brand specializes in footwear for action sports such as skateboarding and snowboarding. The company also manufactures apparel, bags, accessories, hats, t-shirts, and posters. History DC was founded in June 1994 by ...

features a heptagram in the letter C. * The seven-pointed star is used as the logo for the international Danish shipping company A.P. Møller – Mærsk A/S, sometimes known simply as

Maersk (), usually known simply as Maersk ( ), is a Danish Freight transport, shipping and logistics company founded in 1904 by Arnold Peter Møller and his father Peter Mærsk Møller. Maersk's business activities include Port operator, port operat ...

. * In

George R. R. Martin George Raymond Richard Martin (born George Raymond Martin; September 20, 1948) also known by the initials G.R.R.M. is an American author, television writer, and television producer. He is best known as the author of the unfinished series of Hi ...

's novel series ''

A Song of Ice and Fire ''A Song of Ice and Fire'' is a series of high fantasy novels by the American author George R. R. Martin. Martin began writing the first volume, ''A Game of Thrones'', in 1991, and published it in 1996. Martin, who originally envisioned the ser ...

'' and its TV version ''

Game of Thrones ''Game of Thrones'' is an American Fantasy television, fantasy Drama (film and television), drama television series created by David Benioff and for HBO. It is an adaptation of ''A Song of Ice and Fire'', a series of high fantasy novels by ...

'', 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 (Finnish band), HIM, released 26 April 2013 in Finland, 29 April 2013 in Europe, and on 30 April 2013 in the US and Canada. It is produced by Hiili Hiilesmaa, and wa ...

''. * 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 musician, singer, songwriter, and record producer. He is best known as the frontman, main vocalist, and lyricist of the rock band Blur (band), Blur and the co-creator and primary musical con ...

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

subculture as an identifier. * The American progressive rock metal band

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

uses an 'open' seven pointed symbol for their fan group. It is 'open' to signify an invitation into the collective unconscious. * An alternate logo of

-based

Children's Press Scholastic Corporation is an American multinational publishing, education, and media company that publishes and distributes books, comics, and educational materials for schools, teachers, parents, children, and other educational institutions. P ...

from 1945 to 1970, having the slogan "Children's Books Are Important".

Variants

File:Heptagram.svg, Interlaced; equivalent to the 7₁ knot

References

Bibliography * Grünbaum, B. and G.C. Shephard; ''

Tilings and patterns ''Tilings and patterns'' is a book by mathematicians Branko Grünbaum and Geoffrey Colin Shephard published in 1987 by W.H. Freeman. The book was 10 years in development, and upon publication it was widely reviewed and highly acclaimed. Structu ...

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

External links

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