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{{Short description|Star polygon with 7 sides}} {{redirect|Elven star|the novel by Margaret Weis and Tracy Hickman|Elven Star}} {{more footnotes needed|date=April 2011}} {{Regular polygon db|Regular star polygon stat table|p7/2}} {{Regular polygon db|Regular star polygon stat table|p7/3}} {{Star polygons}} A '''heptagram''', '''septagram''', '''septegram''' or '''septogram''' is a seven-point [[star polygon|star]] drawn with seven straight strokes. The name ''heptagram'' combines a [[numeral prefix]], ''[[hepta-]]'', with the [[Greek language|Greek]] suffix ''[[wikt:-gram|-gram]]''. The ''-gram'' suffix derives from ''γραμμῆ'' (''grammē'') meaning a line.<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dgrammh%2F γραμμή], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus</ref> ==Geometry== In general, a heptagram is any self-intersecting [[heptagon]] (7-sided [[polygon]]). There are two ''regular'' heptagrams, labeled as {7/2} and {7/3}, with the second number representing the vertex interval step from a regular [[heptagon]], {7/1}. This is the smallest star polygon that can be drawn in two forms, as [[irreducible fraction]]s. The two heptagrams are sometimes called the ''heptagram'' (for {7/2}) and the ''great heptagram'' (for {7/3}). The previous one, the regular [[hexagram]] {6/2}, is a compound of two triangles. The smallest star polygon is the {5/2} [[pentagram]]. The next one is the {8/3} [[octagram]] and its related {8/2} star figure (a compound of two squares), followed by the regular [[enneagram (geometry)|enneagram]], which also has two forms: {9/2} and {9/4}, as well as one compound of three triangles {9/3}. {| class="wikitable" |- align=center |[[File:Obtuse heptagram.svg|80px]]<br />{7/2} |[[File:Acute heptagram.svg|80px]]<br />{7/3} |[[File:Heptagrams.svg|80px]]<br />{7}+{7/2}+{7/3} |- align=center |[[File:Heptagrammic prism 7-2.png|80px]]<br />7-2 prism |[[File:Heptagrammic prism 7-3.png|80px]]<br />7-3 prism |[[File:6-simplex t0.svg|80px]]<BR>[[Complete graph]] |- align=center |[[File:Antiprism 7-2.png|80px]]<BR>7-2 antiprism |[[File:Antiprism 7-3.png|80px]]<BR>7-3 antiprism |[[File:Antiprism 7-4.png|80px]]<BR>7-4 antiprism |} ==Uses== {{more citations needed section|date=November 2016}} ===Flags and heraldry=== <gallery> 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 [[Félibrige|Felibritge]] on the [[Occitania|Occitan]] flag. File:Flag of Jordan.svg|The Jordanian flag, bearing the star that symbolizes [[Al-Fatiha]] File:Flag of Hokkaido Prefecture.svg|Symbol of [[Hokkaido]] File:Emblem of Samarkand.svg|Coat of arms of [[Samarkand]] File:Commonwealth_Star.svg|Commonwealth Star as the crest of [[Coat of Arms of Australia]] File:Flag of Cook County, Illinois.svg|The flag of [[Cook County]], [[Illinois]], adopted in June 2022 and taking design cues from the [[Flag of Chicago|Flag of]] [[Chicago]], its [[county seat]] File:CHE_Thun_Flag.svg|The coat of arms and flag of [[Thun]] Switzerland </gallery> * The seven-pointed star is incorporated into the flags of various bands of [[Cherokee Indians]] 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]] contains a seven-pointed star. * The [[Flag of Australia]] employs five heptagrams and one [[pentagram]] to depict the [[Crux|Southern Cross]] constellation and the [[Commonwealth Star]]. * Some old versions of the [[coat of arms of Georgia]] including the [[Georgian Soviet Socialist Republic]] used the {7/2} heptagram as an element. * A seven-pointed star is used as the [[badge]] in many sheriff's departments and some smaller-community police departments. *A seven-pointed star is used in the [[otherkin]] pride flag. === Law enforcement === <gallery> File:Seal of the California Highway Patrol.svg|Seal of the [[:California Highway Patrol]] </gallery> ===Religious and occult symbolism=== [[File:Babalon seal.png|thumb|right|Seal of Babalon and the A∴A∴]] * The heptagram became a traditional symbol for warding off evil in Catholicism. * The symbol is also used in [[Kabbalah|Kabbalist]] Judaism. * The heptagram is used in the symbol for [[Babalon]] in Aleister Crowley's occult system [[Thelema]]. * The heptagram is known among [[modern paganism|neopagan]]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]] also uses the symbol, where it is referred to as a ''septegram''. The second heptagram is a symbol of [[magic (paranormal)|magical power]] in some [[pagan]] spiritualities. * In [[alchemy]], 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]]. For example, the [[planetary hours]], from which comes the [[names of the days of the week]]. * 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.<ref>{{Cite web|url=https://www.huna.org/|title=HUNA INTERNATIONAL - Your best resource for Huna Knowledge and Practice|website=www.huna.org}}</ref><ref>{{Cite book|isbn = 0835600025|title = Children of the Rainbow: A Book Concerning the Religion, Legends, and Gods of the Natives of Pre-Christian Hawaii|last1 = Melville|first1 = Leinani|year = 1969| publisher=Theosophical Publishing House }}</ref> * 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=== [[File:Maersk Group Logo.svg|thumb|Logo of [[Maersk]]]] * The logo of American shoe brand [[DC Shoes]] 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. Møller – Mærsk A/S, sometimes known simply as [[Maersk]]. * In [[George R. R. Martin]]'s novel series ''[[A Song of Ice and Fire]]'' and its TV version ''[[Game of Thrones]]'', a seven-pointed star serves as the symbol of the [[Themes in A Song of Ice and Fire#Faith of the Seven|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 (Finnish band)|HIM]] used a heptagram on the cover of their eighth studio album ''[[Tears on Tape]]''. * American heavy metal band [[Darkest Hour (band)|Darkest Hour]] used a heptagram on the cover of their eighth studio album ''[[Darkest Hour (album)|Darkest Hour]]''. * English singer [[Damon Albarn]] uses a heptagram as a symbol in his solo performances and with his band [[Blur (band)|Blur]]. * The {7/3} heptagram is used by some members of the [[otherkin]] subculture as an identifier. * The American progressive rock metal band [[Tool (band)|Tool]] 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 [[Chicago]]-based [[Scholastic Corporation#Imprints and corporate divisions|Children's Press]] from 1945 to 1970, having the slogan "Children's Books Are Important". === Variants === <gallery> File:Heptagram.svg|Interlaced; equivalent to the [[71 knot|7<sub>1</sub> knot]] </gallery> ==See also== * [[Grünbaum–Rigby configuration]] * [[Star polygon]] * [[Stellation#Stellating polygons|Stellated polygons]] * [[List of regular polytopes#Two-dimensional regular polytopes|Two-dimensional regular polytopes]] * [[Major (United States)]] insignia of seven leaves ==References== {{reflist}} '''Bibliography''' * [[Branko Grünbaum|Grünbaum, B.]] and G.C. Shephard; ''[[Tilings and patterns]]'', New York: W. H. Freeman & Co., (1987), {{ISBN|0-7167-1193-1}}. * [[Branko Grünbaum|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 Horton Conway|John H. Conway]], Heidi Burgiel, Chaim Goodman-Strauss, ''The Symmetries of Things'' 2008, {{ISBN|978-1-56881-220-5}} (Chapter 26. pp. 404: Regular star-polytopes Dimension 2) ==External links== * {{Mathworld |urlname=Heptagram |title=Heptagram}} * [http://home.hiwaay.net/~jalison/hepta.html Approximate construction method] {{Polygons}} [[Category:Star polygons|07]] [[Category:7 (number)]]
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