View source for Pentagram

{{Short description|Five-pointed star polygon}}
{{About|the shape with intersecting lines|the shape showing only the outline|Five-pointed star|other uses}}
{{Use dmy dates|date=July 2019}}
[[File:Five Pointed Star Lined.svg|thumb|upright=1.2|Pentagram]]
A '''pentagram''' (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed [[star polygon]], formed from the diagonal [[line segment]]s of a convex (or simple, or non-self-intersecting) [[regular pentagon]]. Drawing a circle around the five points creates a similar symbol referred to as the [[pentacle]],<ref>{{Cite web|author=Gene Brown|title=Difference Between Pentagram and Pentacle|website=Difference Between|date=n.d.|url=http://www.differencebetween.net/miscellaneous/difference-between-pentagram-and-pentacle/|access-date=2023-06-29}}</ref> which is used widely by [[Wicca]]ns and in [[paganism]], or as a sign of life and connections. 

The word ''pentagram'' comes from the [[Greek language|Greek]] word πεντάγραμμον (''pentagrammon''),<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dpenta%2Fgrammon πεντάγραμμον], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus;  a  noun form of adjectival  πεντάγραμμος (''pentagrammos'') or πεντέγραμμος (''pentegrammos''), a word meaning roughly "five-lined" or "five lines"</ref> from πέντε (''pente''), "five" + γραμμή (''grammē''), "line".<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dpe%2Fnte πέντε], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus;  Satan all 3 names mentioned before daylight full [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>
The word pentagram refers to just the star and the word [[pentacle]] refers to the star within a circle, although there is some overlap in usage.<ref>this usage is borne out by the Oxford English Dictionary, although that work specifies that a circumscription makes the form of a five-pointed star and its etymon post-classical Latin ''pentaculum '' [...]   A pentagram, esp. one enclosed in a circle; a talisman or magical symbol in the shape of or inscribed with a pentagram. Also, in extended use: any similar magical symbol (freq. applied to a hexagram formed by two intersecting or interlaced equilateral triangles)."</ref> The word ''pentalpha'' is a 17th-century revival of a post-classical Greek name of the shape.<ref>πένταλφα, "five Alphas", interpreting the shape as five Α shapes overlapping at 72-degree angles.</ref>

==History==

===Early history===
Early pentagrams have been found on Sumerian pottery from Ur c. 3500 [[Common Era|BCE]], and the five-pointed star was at various times the symbol of [[Ishtar]] or [[Marduk]].<ref>{{cite book |last=Budge |first=Sir E. A. Wallis |title=Amulets and Talismans |date=1968 |pages=433}}</ref><ref>{{cite web |last=Scott |first=Dustin Jon |date=2006 |title=History of the Pentagram |url=https://djonscott.com/pent-hist.html |access-date=18 May 2021 |website= |publisher= |quote=}}</ref>[[File:Hugieia-pentagram.svg|thumb|A Pythagorean "Hugieia Pentagram"<ref>Allman, G. J., ''Greek Geometry From Thales to Euclid'' (1889), p.26.</ref>]]
[[File:Right-handed interlaced pentagram.svg|thumb|A right-handed interlaced pentagram, popular with Wiccans and some other neo-pagans. The [[Flag of Morocco]] often bears [[:File:Left-handed interlaced pentagram.svg|the left-handed version]].]]

Pentagram symbols from about 5,000 years ago were found in the [[Liangzhu culture]] of [[China]].<ref>{{Cite web |url=https://fashion.chinadaily.com.cn/a/201909/23/WS5d885fd5a31099ab995e19ea.html |title=距今5000年！良渚文物中發現最古老五角星圖案 |author=馬愛平 |date= September 23, 2019 |publisher=China Daily |language=Chinese |accessdate= |quote= }}</ref><ref name="Minzhen">{{cite news |last1=Chen |first1=Minzhen |title=Chinese antiques give new insight into history of pentagram |url=http://www.csstoday.com/Item/12413.aspx |access-date=1 December 2024 |work=Chinese Social Sciences Today |publisher=Social Sciences in China Press |date=2024}}</ref>  A pentagram appeared in a Chinese text on music theory from the [[Warring States period]] ({{circa|475}}{{snd}}221&nbsp;BC) as a diagram of the mathematical relations between the five notes in a particular [[Chinese musicology#Music scales|Chinese musical scale]].<ref name="Minzhen" />

The pentagram was known to the [[ancient Greeks]], with a depiction on a vase possibly dating back to the 7th century BCE.<ref>Coxeter, H.S.M.; ''Regular Polytopes'', 3rd edn, Dover, 1973, p. 114.</ref> [[Pythagoreanism]] originated in the 6th century BCE and used the pentagram as a symbol of mutual recognition, of wellbeing, and to recognize good deeds and charity.<ref>Ball, W. W. Rouse and Coxeter, H. S. M.; ''Mathematical Recreations and Essays'', 13th Edn., Dover, 1987, p. 176.</ref>

From around 300–150 BCE the pentagram stood as the symbol of Jerusalem, marked by the 5 Hebrew letters ירשלם spelling its name.<ref>{{Cite web|url=https://aboutjewishpeople.com/star-of-david-vs-pentagram/|title=Star of David vs. Pentagram: Everything You Need to Know|date=17 July 2020}}</ref>

In [[Neoplatonism]], the pentagram was said to have been used as a symbol or sign of recognition by the  [[Pythagoreans]], who called the pentagram {{lang|grc|ὑγιεία }} {{lang|grc-Latn|[[Hygieia|hugieia]]}} "health".<ref>Allman, G. J., ''Greek Geometry From Thales to Euclid'', part I (1877), in ''Hermathena'' 3.5, pp. [https://archive.org/stream/greekgeometryfro00allmuoft#page/n31/mode/2upp. 183], [https://archive.org/stream/greekgeometryfro00allmuoft#page/n45/mode/2up 197], citing [[Iamblichus]] and the Scholiast on Aristophanes. The pentagram was said to have been so called from Pythagoras himself having written the letters Υ, Γ, Ι, Θ (= /ei/), Α on its vertices.</ref><ref name="DeOcc">{{cite book |last1=Agrippa von Nettesheim |first1=Heinrich Cornelius |title=De occulta philosophia libri tres |date=1533 |location=Cologne |pages=160, 163, 276-277 |url=https://www.loc.gov/resource/rbc0001.2009gen12345/?sp=280 |access-date=28 November 2024 |quote={{lang|la|eius generis sunt signaculum Constantino ostensum, quod crucem plerique appelabant, Latinis literis inscriptum, 'in hoc vince', et alterum revelatum Antiocho cognomine Soteris, in figura pentagoni, quod sanitatem edicit, nam resolutum in literas, edicit vocabulum ὑγίεα, id est, 'sanitas', in quorum signorum fidutia et virtute, uterque regum insignem contra hostes victoriam reportauit.  Sic Iudas qui ob eam rem postea cognominatus est Machabaeus, cum Iudaeis pugnaturus contra Antiochum Eupatorem, nobile illud signaculum מׄכׄבׄיׄ ad angelum accepit,}}}}</ref>

===Western symbolism===
====Middle Ages====
The pentagram was used in ancient times as a Christian symbol for the five [[sense]]s,<ref>''Christian Symbols Ancient and Modern'', Child, Heather and Dorothy Colles. New York: Charles Scribner's Sons, 1971, {{isbn|0-7135-1960-6}}.</ref> or of the [[Five Holy Wounds|five wounds of Christ]]. The pentagram plays an important symbolic role in the 14th-century English poem ''[[Sir Gawain and the Green Knight]]'', in which the symbol decorates the shield of the hero, [[Gawain]]. The [[Gawain Poet|unnamed poet]] credits the symbol's origin to King [[Solomon]], and explains that each of the five interconnected points represents a virtue tied to a group of five: Gawain is perfect in his [[five senses]] and five fingers, faithful to the Five Wounds of Christ, takes courage from the [[five joys]] that [[Mary, mother of Jesus|Mary]] had of Jesus, and exemplifies the five virtues of [[knight]]hood,<ref>{{cite journal |last1=Morgan |first1=Gerald |date=1979 |title=The Significance of the Pentangle Symbolism in "Sir Gawain and the Green Knight" |journal=The Modern Language Review |volume=74 |issue=4 |pages=769–790 |doi=10.2307/3728227 |jstor=3728227}}<!--|access-date=28 June 2013--></ref> which are generosity, friendship, chastity, chivalry, and piety.<ref>''Sir Gawain and the Green Knight'', lines 619–665</ref>
[[File:Amiens Rose Nord 1.jpg|thumb|left|upright|The North rose of [[Amiens Cathedral]]]]
The North rose of [[Amiens Cathedral]] (built in the 13th century) exhibits a pentagram-based motif. Some sources interpret the unusual downward-pointing star as symbolizing the Holy Spirit descending on people.

====Renaissance====
[[Heinrich Cornelius Agrippa]] and others perpetuated the popularity of the pentagram as a magic symbol, attributing the five neoplatonic elements to the five points, in typical Renaissance fashion.  Agrippa depicts the human body inscribed in an 'upright' (point-up) pentagram and another with its hands in rotated pentagrams, among numerous other geometrical figures, in the section on 'the proportions and harmonious measures of the human body', and an 'inverted' (point-down) version of the Pythagorean 'hygeia' pentagram in the section on 'characters, received only by revelation, which no other kind of reasoning can discover', alongside variations of the [[Chi-Rho]] and the Hebrew word [[Judas Maccabeus#Origin of the name "The Hammer"|Makabi]].

'Of this type are the signet shown to [[Constantine I|Constantine]], which most people called a cross, inscribed in Latin letters, '[[In hoc signo vinces|in this conquer]]', and another revealed to [[Antiochus I Soter|Antiochus who was surnamed Soteris]], in the shape of a pentagon, which issued health, for resolved into letters, it issued the word ὑγίεα, that is, 'health', in the confidence and virtue of which signs, each of the kings won a notable victory against their enemies.  Thus Judas, who for this reason was afterwards known as Maccabeus, was about to fight with the Jews against Antiochus Eupatorus, and received that noble seal מׄכׄבׄיׄ from the angel'.<ref name="DeOcc" />

====Romanticism====
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 but controversial writer [[Éliphas Lévi]], known for believing that magic was a real science, had 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."<ref>{{cite book |title=Transcendental Magic, its Doctrine and Ritual |trans-title=Dogme et rituel de la haute magie |publisher=[[Red Wheel/Weiser/Conari|Weiser]] |location=[[York Beach, Maine|York Beach]] |first=Éliphas |last=Lévi |author-link=Éliphas Lévi |others=Trans. by [[A. E. Waite]] |date=1999 |orig-year=1896 (translated), 1854 (first published) |oclc=263626874}}</ref>
*"The flaming star, which, when turned upside down, is the {{sic|heirol|gyphic}} 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 a sign of antagonism and fatality. It is the goat of lust attacking the heavens with its horns."<ref>{{cite book |title=The Key of the Mysteries |trans-title=la Clef des grands mystères suivant Hénoch, Abraham, Hermès Trismégiste et Salomon |publisher=[[Red Wheel/Weiser/Conari|Weiser]] |location=Boston |first=Éliphas |last=Lévi |author-link=Éliphas Lévi |others=Trans. by [[Aleister Crowley]] |page=69 |date=2002 |orig-year=1939 (translated), 1859 (first published) |oclc=49053462}}</ref>
*"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."<ref>{{cite book |title=Magic, White and Black |publisher=The Path |location=New York |first=Franz |last=Hartmann |author-link=Franz Hartmann |edition=5th |date=1895 |orig-year=1886 |oclc=476635673}}</ref>

<gallery class="center">
File:Pentagram and human body (Agrippa).jpg|Man inscribed in a pentagram, from [[Heinrich Cornelius Agrippa]]'s ''[[Three Books of Occult Philosophy|De occulta philosophia libri tres]]''. The five signs at the pentagram's [[vertex (geometry)|vertices]] are [[astrological]].
File:Inverted pentacle.PNG|Another pentagram from Agrippa's book. This one has the Pythagorean letters inscribed around the circle.
File:Pentagram (Levi).jpg|The [[occult]]ist and [[Magician (paranormal)|magician]] [[Éliphas Lévi]]'s pentagram, which he considered to be a symbol of the [[Macrocosm and microcosm|microcosm]], or human
</gallery>{{Star polygons}}

The [[apotropaic]] (protective) use in [[German folklore]] of the pentagram symbol (called ''[[Drudenfuss]]'' in German) is referred to by [[Goethe]] in ''[[Faust, Part One|Faust]]'' (1808), where a pentagram prevents [[Mephistopheles]] from leaving a room (but did not prevent him from entering by the same way, as the outward pointing corner of the diagram happened to be imperfectly drawn):
{{blockquote|
Mephistopheles:
:I must confess, I'm prevented though
:By a little thing that hinders me,
:The Druid's-foot on your doorsill–
Faust:
:The Pentagram gives you pain?
:Then tell me, you Son of Hell,
:If that's the case, how did you gain
:Entry? Are spirits like you cheated?

Mephistopheles:
:Look carefully! It's not completed:
:One angle, if you inspect it closely
:Has, as you see, been left a little open.<ref>{{Cite web|title=Goethe, Johann Wolfgang von (1749–1832) - Faust, Part I: Scenes I to III|url=https://www.poetryintranslation.com/PITBR/German/FaustIScenesItoIII.php|access-date=2021-05-25|website=www.poetryintranslation.com}}</ref>}}

Also protective is the use in [[Icelandic folklore]] of a gestured or carved rather than painted pentagram (called {{lang|is|smèrhnút}} in Icelandic), according to 19th century folklorist [[Jón Árnason (author)|Jón Árnason]]:<ref>{{cite book|first=Jón |last=Árnason |author-link=Jón Árnason (author)|date=1862 |language=is|chapter={{lang|is|Töfrabrogð}} [Magic trick]|title=Íslenzkar Þjoðsögur og Æfintýri |trans-title=Icelandic Folktales and Legends |volume=1 |location=[[Leipzig]] |publisher=J. C. Hinrich's Bookstore |page=432 |url=https://baekur.is/bok/d1007e0b-6463-47a4-9e8d-ce48e82042e7/1/472/Islenzkar_thjodsogur_og#page/n471/mode/1up |quote={{lang|is|Smèr það, er verður af tilberaspýunni, er kallað tilberasmèr; er það útlits sem annað smèr; en gjöri maður krossmark yfir því, eða risti á það kross, eða mynd þá, er smèrhnútur heitir,<sup>*</sup> springur það alt í smámola og verður eins og draflakyrníngur, svo ekki sèst eptir af því, nema agnir einar, eða það hjaðnar niður sem froða. Þykir það því varlegra, ef manni er boðið óhrjálegt smèr að borða, eða í gjöld, að gjóra annaðhvort þetta mark á það, því tilberasmèr þolir hvorki krossmark né smjörhnút.&nbsp;/ *&nbsp;Smèrhnútur er svo í lögun:&nbsp;[[File:Five_Pointed_Star_Lined.svg|15px]]}}}}</ref>
:A butter that comes from the fake vomit is called a fake butter; it looks like any other butter; but if one makes a sign of a cross over it, or carves a cross on it, or a figure called a buttermilk-knot,<sup>*</sup> it all explodes into small pieces and becomes like a grain of dross, so that nothing remains of it, except only particles, or it subsides like foam. Therefore it seems more prudent, if a person is offered a horrible butter to eat, or as a fee,<ref>In the Middle Ages, butter was used for payment, e.g. rent. See:<br>•&nbsp;{{cite book |last=Sexton |first=Regina |chapter=The Role and Function of Butter in the Diet of the Monk and Penitent in Early Medieval Ireland |title=The Fat of the Land: Proceedings of the Oxford Symposium on Food and Cooking 2002 |editor-last=Walker |editor-first=Harlan |location=Bristol |publisher=Footwork |date=2003 |pages=253–269 |chapter-url=https://books.google.com/books?id=ZJ5qBQAAQBAJ&pg=PT259}}</ref> to make either mark on it, because a fake butter cannot withstand either a cross mark or a butter-knot.
:&ast;&nbsp;The butter-knot is shaped like this:&nbsp;[[File:Five_Pointed_Star_Lined.svg|15px]]<!-- Possibly "small-knot" or "buttermilk-knot" rather than "butter-knot"; the word 'smèr' is ambiguous. However, 'smjör' is clearly butter. -->

===Uses in modern occultism===
Based on Renaissance-era occultism, the pentagram found its way into the symbolism of modern occultists. Its major use is a continuation of the ancient Babylonian use of the pentagram as an [[apotropaic charm]] to protect against evil forces.<ref>{{cite book |url=https://books.google.com/books?id=zwAlAAAAMAAJ |title=The Pentagram as Medical Symbol: An Iconological Study |publisher=Hes & De Graaf |first=Jan |last=Schouten |page=18 |date=1968 |isbn=978-90-6004-166-6}}</ref> Éliphas Lévi claimed that "The Pentagram expresses the mind's domination over the elements and it is by this sign that we bind the demons of the air, the spirits of fire, the spectres of water, and the ghosts of earth."<ref>{{cite book |url=https://books.google.com/books?id=jX9BAAAAYAAJ&pg=PA136 |title=The Mysteries of Magic: A Digest of the Writings of Eliphas Lévi |publisher=George Redway |location=London |first=Arthur Edward |last=Waite |pages=136 |date=1886}}</ref> In this spirit, the [[Hermetic Order of the Golden Dawn]] developed the use of the pentagram in the [[lesser banishing ritual of the pentagram]], which is still used to this day by those who practice Golden Dawn-type magic.

[[Aleister Crowley]] made use of the pentagram in the system of [[magick]] used in [[Thelema]]: an adverse or inverted pentagram represents the descent of spirit into matter, according to the interpretation of [[Lon Milo DuQuette]].<ref>{{cite book |url=https://books.google.com/books?id=-07yFC31j6wC&pg=PA93 |title=The Magick of Aleister Crowley: A Handbook of the Rituals of Thelema |publisher=Weiser Books |first=Lon Milo |last=DuQuette |pages=93, 247 |date=2003 |isbn=978-1-57863-299-2}}</ref> Crowley contradicted his old comrades in the [[Hermetic Order of the Golden Dawn]], who, following Levi, considered this orientation of the symbol [[evil]] and associated it with the triumph of matter over spirit.

===Use in new religious movements===

====Baháʼí Faith====
{{Main|Baháʼí symbols}}
[[File:Bab-Star-Tablet-Haykal.jpg|thumb|upright=0.8|Haykal by the [[Báb]] written in his own hand]]
The five-pointed star is a symbol of the [[Baháʼí Faith]].<ref>{{Cite web|url=https://reference.bahai.org/en/t/se/DG/dg-141.html.utf8|title=Bahá'í Reference Library - Directives from the Guardian, Pages 51-52|website=reference.bahai.org}}</ref><ref>{{Cite web|url=https://bahai-library.com/uhj_nine_pointed_star|title=The Nine-Pointed Star|website=bahai-library.com}}</ref> In the Baháʼí Faith, the star is known as the ''Haykal'' ({{langx|ar|"temple"}}), and it was initiated and established by the [[Báb]]. The Báb and [[Bahá'u'lláh]] wrote various works in the form of a pentagram.<ref name="Momen">[[Momen, Moojan|Moojan Momen]] (2019). ''[https://blogs.bl.uk/asian-and-african/2019/10/the-star-tablet-of-the-bab.html The Star Tablet of the Bab].'' British Library Blog.</ref><ref name="bayat">Bayat, Mohamad Ghasem (2001). ''[https://bahai-library.com/bayat_surat_haykal An Introduction to the Súratu'l-Haykal (Discourse of The Temple)]'' in Lights of Irfan, Book 2.</ref>

====The Church of Jesus Christ of Latter-day Saints====
[[The Church of Jesus Christ of Latter-day Saints]] is theorized to have begun using both upright and inverted five-pointed stars in [[Temple (Latter Day Saints)|Temple]] architecture, dating from the [[Nauvoo Illinois Temple]] dedicated on 30 April 1846.<ref>See the [http://users.marshall.edu/~brown/nauvoo/nt-parent.html Nauvoo Temple] {{Webarchive|url=https://web.archive.org/web/20200517215640/http://users.marshall.edu/~brown/nauvoo/nt-parent.html |date=17 May 2020 }} website discussing its architecture, and particularly the page on [http://users.marshall.edu/~brown/nauvoo/symbols.html Nauvoo Temple exterior symbolism] {{Webarchive|url=https://web.archive.org/web/20200517215640/http://users.marshall.edu/~brown/nauvoo/nt-parent.html |date=17 May 2020 }}. Retrieved 16 December 2006.</ref> Other temples decorated with five-pointed stars in both orientations include the [[Salt Lake Temple]] and the [[Logan Utah Temple]]. These usages come from the symbolism found in [[Book of Revelation|Revelation]] chapter 12: "And there appeared a great wonder in heaven; a woman clothed with the sun, and the moon under her feet, and upon her head a crown of twelve stars."<ref>{{cite web |url=http://www.fairlds.org/pubs/Stars.pdf |title=Inverted Stars on LDS Temples |work=FAIRLDS.org |first=Matthew B |last=Brown |author-link=Matthew B. Brown |date=2002 |archive-url=https://web.archive.org/web/20080229073604/http://www.fairlds.org/pubs/Stars.pdf |archive-date=29 February 2008}}</ref>

====Wicca====
{{multiple image |align=right |direction=horizontal |total_width=300
 |image1=Pentacle (fixed width).svg |caption1=Typical Neopagan pentagram (circumscribed)
 |image2=USVA headstone emb-37.svg |caption2=[[United States Department of Veterans Affairs emblems for headstones and markers|USVA]] headstone emblem 37
}}
Because of a perceived association with Satanism and occultism, many United States schools in the late 1990s sought to prevent students from displaying the pentagram on clothing or jewelry.<ref>[http://www.religioustolerance.org/sch_clot5.htm "Religious Clothing in School"], Robinson, B.A., Ontario Consultants on Religious Tolerance, 20 August 1999, updated 29 April 2005. Retrieved 10 February 2006. {{cite press release |url=http://aclumich.org/modules.php?name=News&file=article&sid=26 |title=ACLU Defends Honor Student Witch Pentacle |publisher=American Civil Liberties Union of Michigan |date=10 February 1999 |access-date=10 February 2006 |url-status=bot: unknown |archive-url=https://web.archive.org/web/20031108123215/http://aclumich.org/modules.php?name=News&file=article&sid=26 |archive-date=8 November 2003}} [http://www.post-gazette.com/magazine/20000927witch2.asp "Witches and wardrobes: Boy says he was suspended from school for wearing magical symbol"] Rouvalis, Cristina; Pittsburgh Post-Gazette, 27 September 2000. Retrieved 10 February 2006.</ref> In public schools, such actions by administrators were determined in 2000 to be in violation of students' [[First Amendment to the United States Constitution|First Amendment]] right to [[Free Exercise Clause|free exercise of religion]].<ref>{{cite web |url=http://www.firstamendmentcenter.org/federal-judge-upholds-indiana-students-right-to-wear-wiccan-symbols |title=Federal judge upholds Indiana students' right to wear Wiccan symbols |agency=Associated Press |date=1 May 2000 |access-date=21 September 2007 |url-status=dead |archive-url=https://swap.stanford.edu/20140330195413/http://www.firstamendmentcenter.org/federal-judge-upholds-indiana-students-right-to-wear-wiccan-symbols |archive-date=30 March 2014}}</ref>

The encircled pentagram (referred to as a [[pentacle]] by the plaintiffs) was added to the list of 38 approved religious symbols to be placed on the tombstones of fallen service members at [[Arlington National Cemetery]] on 24 April 2007. The decision was made following ten applications from families of fallen soldiers who practiced [[Wicca]]. The government paid the families {{US$|225,000}} to settle their pending lawsuits.<ref>{{cite news |url=http://www.cnn.com/2007/US/04/23/wiccan.grave.ap/index.html |title=Wiccan symbol OK for soldiers' graves |publisher=[[CNN|CNN.com]] |agency=Associated Press |date=23 April 2007 |archive-url=https://web.archive.org/web/20070426075801/http://www.cnn.com/2007/US/04/23/wiccan.grave.ap/index.html |archive-date=26 April 2007}}</ref><ref>{{cite web |url=http://www.cem.va.gov/hmm/emblems.asp |title=Burial and Memorials: Available Emblems of Belief for Placement on Government Headstones and Markers |publisher=[[United States Department of Veterans Affairs]] |date=3 July 2013 |access-date=13 January 2014}}</ref>

===Other religious use===

==== Satanism ====
{{multiple image
| align             = right
| direction         = horizontal
| total_width       = 300
| image1            = Pentagram4.svg
| caption1          = The inverted pentagram is the most notable and widespread symbol of [[Satanism]].
| image2            = Baphomet Pentagram.svg
| caption2          = The goat head of [[Baphomet]] forms an inverted pentagram, as depicted in the [[Sigil of Baphomet]]
}}

The inverted pentagram is broadly used in [[Satanism]], sometimes depicted with the [[goat]]'s head of [[Baphomet]], as popularized by the [[Church of Satan]] since 1968. [[LaVeyan Satanism|LaVeyan Satanists]] pair the goat head with Hebrew letters at the five points of the pentagram to form the [[Sigil of Baphomet]]. The Baphomet sigil was adapted for the [[Joy of Satan Ministries]] logo, using [[cuneiform]] characters at the five points of the pentagram, reflecting the shape's earliest use in [[Sumeria]]. The inverted pentagram also appears in [[The Satanic Temple]] logo, with an alternative depiction of Baphomet's head. Other depictions of the Satanic goat's head resemble the inverted pentagram without its explicit outline.

====Serer religion====
The five-pointed star is a symbol of the [[Serer religion]] and the [[Serer people]] of West Africa. Called ''Yoonir'' in [[Serer language|their language]], it symbolizes the universe in the [[Serer creation myth]], and also represents the star [[Sirius]].<ref>{{Cite book |title=La civilisation Sereer, Volume II: Pangool |series=Nouvelles éditions Africaines du Sénégal |location=Dakar, Senegal |language=fr |first=Henry |last=Gravrand |author-link=Henry Gravrand |year=1990 |isbn=2-7236-1055-1 |page=20}}</ref><ref name="Museum of Civilization">{{cite book |title=Tracing Memory: A Glossary of Graphic Signs and Symbols in African Art and Culture |series=Mercury series, no. 71 |publisher=Canadian Museum of Civilization |location=Hull, Québec |first=Clémentine Faïk-Nzuji |last=Madiya |author-link=Clémentine Nzuji |pages=27, 155 |date=1996 |isbn=0-660-15965-1}}</ref>

===Other modern use===
*The pentagram is featured on the national flags of [[flag of Morocco|Morocco]] (adopted 1915) and [[flag of Ethiopia|Ethiopia]] (adopted 1996 and readopted 2009)
<gallery class="center">
Image:Flag of Morocco (large stroke).svg|[[Morocco]]'s flag
Image:Flag of Ethiopia.svg|[[Ethiopia]]'s flag
</gallery>

*The [[Order of the Eastern Star]], an organization (established 1850) associated with [[Freemasonry]], uses a pentagram as its symbol, with the five [[isosceles triangle]]s of the points colored blue, yellow, white, green, and red.  In most Grand Chapters the pentagram is used pointing down, but in a few, it is pointing up. Grand Chapter officers often have a pentagon inscribed around the star<ref>Ritual of the Order of the  Eastern Star, 1976</ref>(the emblem shown here is from the Prince Hall Association).
<gallery class="center">
Image:OrderEasternStar logo from saucer.jpg| [[Order of the Eastern Star]] emblem
</gallery>

*A pentagram is featured on the flag of the [[Netherlands|Dutch]] city of [[Haaksbergen]], as well on its coat of arms.
<gallery class="center">
Image:Flag of Haaksbergen.svg| Flag of Haaksbergen
</gallery>

*A pentagram is featured on the flag of the [[Japan]]ese city of [[Nagasaki]], as well on its emblem.
<gallery class="center">
Image:Flag of Nagasaki, Nagasaki.svg| Flag of Nagasaki
</gallery>

==Geometry==<!--This section is linked from [[Golden ratio]]-->
[[File:Stellamerlata.gif|thumb|[[Koch snowflake]]s drawn with [[MSWLogo]] (in Tartapelago<ref>{{cite web|url=http://www.pietrocola.eu/maecla/tartapelago/frattali/index.htm |title=Tartapelago. Exposure of fractals|first=Giorgio|last=Pietrocola |date=2005 |website=Maecla  }}</ref>) ]]
[[File:Pentagram Angles Notation.svg|thumb|Drawing of a pentagram with notations of its angles.]]

The pentagram is the simplest [[regular polygon|regular]] [[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]] the [[dihedral group]] of order 10.

It can be seen as a net of a [[pentagonal pyramid]] although with isosceles triangles.

===Construction===
The pentagram can be constructed by connecting alternate vertices of a [[pentagon]]; see [[Pentagon#Construction of a regular pentagon|details of the construction]]. It can also be constructed as a [[stellation]] of a pentagon, by extending the edges of a pentagon until the lines intersect.

===Golden ratio===
[[Image:Pentagram-phi.svg|thumb|A regular pentagram colored to distinguish its line segments of different lengths. The four lengths are in [[golden ratio]] to one another.]]
The [[golden ratio]], ''φ'' = (1 + {{radic|5}}) / 2 ≈ 1.618, satisfying:
:<math>\varphi=1+2\sin(\pi/10)=1+2\sin 18^\circ\,</math>
:<math>\varphi=1/(2\sin(\pi/10))=1/(2\sin 18^\circ)\,</math>
:<math>\varphi=2\cos(\pi/5)=2\cos 36^\circ\,</math>
plays an important role in regular pentagons and pentagrams. Each intersection of edges sections the edges in the 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 two intersecting edges (a side of the pentagon in the pentagram's center) is ''φ''. As the four-color illustration shows:
:<math>\frac{\mathrm{red}}{\mathrm{green}} = \frac{\mathrm{green}}{\mathrm{blue}} = \frac{\mathrm{blue}}{\mathrm{magenta}} = \varphi.</math>

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

===Trigonometric values===
{{main|Exact trigonometric values}}
:<math>
\begin{align}
\sin \frac{\pi}{10} & = \sin 18^\circ = \frac{\sqrt 5 - 1}{4}=\frac{\varphi-1}{2}=\frac{1}{2\varphi} \\[5pt]
\cos \frac{\pi}{10} & = \cos 18^\circ = \frac{\sqrt{2(5 + \sqrt 5)}}{4} \\[5pt]
\tan \frac{\pi}{10} & = \tan 18^\circ = \frac{\sqrt{5(5 - 2 \sqrt 5)}}{5} \\[5pt]
\cot \frac{\pi}{10} & = \cot 18^\circ = \sqrt{5 + 2 \sqrt 5} \\[5pt]
\sin \frac{\pi}{5} & = \sin 36^\circ = \frac{\sqrt{2(5 - \sqrt 5)} }{4} \\[5pt]
\cos \frac{\pi}{5} & = \cos 36^\circ = \frac{\sqrt 5+1}{4} = \frac{\varphi}{2} \\[5pt]
\tan \frac{\pi}{5} & = \tan 36^\circ =  \sqrt{5 - 2\sqrt 5} \\[5pt]
\cot \frac{\pi}{5} & = \cot 36^\circ = \frac{ \sqrt{5(5 + 2\sqrt 5)}}{5}
\end{align}
</math>

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.

===Spherical pentagram===
{{Further| Pentagramma mirificum}}
A pentagram can be drawn as a [[star polygon]] on a sphere, composed of five great circle arcs, whose all internal angles are right angles. This shape was described by [[John Napier]] in his 1614 book ''Mirifici logarithmorum canonis descriptio'' (Description of the wonderful rule of logarithms) along with rules that link the values of trigonometric functions of five parts of a right spherical triangle (two angles and three sides). It was studied later by [[Carl Friedrich Gauss]].

===Three-dimensional figures===
{{Further|Uniform polyhedron#Icosahedral symmetry{{!}}Uniform polyhedron: Icosahedral symmetry}}
Several [[polyhedra]] incorporate pentagrams:
<gallery>
Image:Pentagrammic prism.png|[[Pentagrammic prism]]
Image:Pentagrammic antiprism.png|[[Pentagrammic antiprism]]
Image:Pentagrammic crossed antiprism.png|[[Pentagrammic crossed-antiprism]]
Image:Small_stellated_dodecahedron.png|[[Small stellated dodecahedron]]
Image:Great_stellated_dodecahedron.png|[[Great stellated dodecahedron]]
Image:Small ditrigonal icosidodecahedron.png|[[Small ditrigonal icosidodecahedron|Small ditrigonal icosidodeca&shy;hedron]]
Image:Dodecadodecahedron.png|[[Dodecadodecahedron]]
</gallery>

===Higher dimensions===
Orthogonal projections of higher dimensional polytopes can also create pentagrammic figures:
{| class=wikitable width=720
!colspan=2|4D
!colspan=2|5D
|-
|[[File:4-simplex t0.svg|180px]]<br />The regular [[5-cell]] (4-[[simplex]]) has five vertices and 10 edges.
|[[File:4-simplex t1.svg|180px]]<br />The [[rectified 5-cell]] has 10 vertices and 30 edges.
|[[File:5-simplex t1 A4.svg|180px]]<br />The [[rectified 5-simplex]] has 15 vertices, seen in this orthogonal projection as three nested pentagrams.
|[[File:5-simplex t2 A4.svg|180px]]<br />The [[birectified 5-simplex]] has 20 vertices, seen in this orthogonal projection as four overlapping pentagrams.
|}

All ten 4-dimensional [[Regular 4-polytope#Regular star (Schläfli–Hess) 4-polytopes|Schläfli–Hess 4-polytopes]] have either pentagrammic faces or [[vertex figure]] elements.

==Pentagram of Venus==
[[File:Venus geocentric orbit curve simplified Line (pentagram).svg|thumb|The pentagram of Venus]]
The pentagram of Venus is the apparent path of the [[planet]] [[Venus]] as observed from [[Earth]]. Successive [[Conjunction (astronomy)#Superior and inferior|inferior conjunction]]s of Venus repeat with an [[orbital resonance]] of approximately 13:8—that is, Venus orbits the [[Sun]] approximately 13 times for every eight orbits of Earth—shifting 144° at each inferior conjunction.<ref>{{cite web |url=https://johncarlosbaez.wordpress.com/2014/01/04/the-pentagram-of-venus |title=The Pentagram of Venus |first=John |last=Baez |author-link=John C. Baez |work=Azimuth |date=4 January 2014 |access-date=7 January 2016 |url-status=dead |archive-url=https://web.archive.org/web/20151214005503/https://johncarlosbaez.wordpress.com/2014/01/04/the-pentagram-of-venus/ |archive-date=14 December 2015}}</ref> The tips of the five loops at the center of the figure have the same geometric relationship to one another as the five [[vertex (geometry)|vertices]], or points, of a pentagram, and each group of five [[intersection]]s [[equidistant]] from the figure's center have the same geometric relationship.

==In computer systems==
{{see also|Unicode input}}
The pentagram has these [[Unicode]] code points that enable them to be included in documents:
* {{unichar|26E4|pentagram}}
* {{unichar|26E5|right-handed interlaced pentagram}}
* {{unichar|26E6|left-handed interlaced pentagram}}
* {{unichar|26E7|inverted pentagram}}

==See also==
{{div col|colwidth=25em}}
* {{Annotated link |Abe no Seimei}}
* {{Annotated link |Christian symbolism}}
* {{Annotated link |Command at Sea insignia}}
* {{Annotated link |Enneagram (geometry)}}
* {{Annotated link |Five-pointed star}}
* {{Annotated link |Heptagram}}
* {{Annotated link |Hexagram}}
* {{Annotated link |Lute of Pythagoras}}
* {{Annotated link |Medal of Honor}}
* [[Pentachoron]] – the 4-[[simplex]]
* {{Annotated link |Pentagram map}}
* {{Annotated link |Pentalpha}}
* {{Annotated link |Petersen graph}}
* {{Annotated link |Ptolemy's theorem}}
* {{Annotated link |Seal of Solomon}}
* {{Annotated link |Star polygons in art and culture}}
* {{Annotated link |Star (heraldry)}}
* {{Annotated link |Stellation#Stellating polygons|Stellated polygons}}
{{div col end}}

==References==
{{Reflist|30em}}

==Further reading==
* {{cite encyclopedia |title=Pentagram |encyclopedia=The Continuum Encyclopedia of Symbols |publisher=Continuum Books |location=New York City |first=Udo |last=Becker |translator-first=Lance W. |translator-last=Garmer |date=1994 |isbn=978-0-8264-0644-6 |url=https://archive.org/details/continuumencyclo00beck/page/230 |pages=230ff |ref=none}}
* {{cite book |chapter=Chapter 26, Higher Still: Regular Star-Polytopes |title=The Symmetries of Things |publisher=A. K. Peters |location=Wellesley, Massachusetts |first1=John Horton |last1=Conway |author1-link=John Horton Conway |first2=Heidi |last2=Burgiel |first3=Chaim |last3=Goodman-Strauss |page=404 |date=April 2008 |isbn=978-1-56881-220-5 |ref=none}}
* {{cite book |title=Signs and Symbols in Christian Art |publisher=Oxford University Press |location=New York City |first=George Wells |last=Ferguson |page=59 |date=1966 |orig-year=1954 |oclc=65081051 |ref=none}}
* {{cite book |title=Tilings and Patterns |publisher=W. H. Freeman |location=New York |first1=Branko |last1=Grünbaum |author1-link=Branko Grünbaum |first2=Geoffrey Colin |last2=Shephard |author2-link=Geoffrey Colin Shephard |date=1987 |isbn=978-0-7167-1193-3 |url=https://archive.org/details/isbn_0716711931 |ref=none}}
* {{cite book |chapter=Polyhedra with Hollow Faces |title=Polytopes: Abstract, Convex and Computational |series=NATO ASI Series C: Mathematical and Physical Sciences |publisher=Springer Netherlands |location=Dordrecht |first1=Branko |last1=Grünbaum |author1-link=Branko Grünbaum |editor1=Bisztriczky, T. |editor2=McMullen, P. |editor2-link=Peter McMullen |editor3=Schneider, A. |editor4=Weiss, A. Ivić |volume=440 |pages=43–70 |date=1994 |isbn=978-94-010-4398-4 |doi=10.1007/978-94-011-0924-6_3 |ref=none}}

==External links==
{{Wikiquote}}
{{Commons category|Pentagrams}}
*{{MathWorld |urlname=Pentagram |title=Pentagram}}
*[http://www.cs.utk.edu/~mclennan/BA/PP.html The Pythagorean Pentacle] from the Biblioteca Arcana.

{{Polygons}}
{{Serer topics|state=collapsed}}
{{Thelema series}}
{{Neopaganism}}
{{Authority control}}

[[Category:Christian symbols]]
[[Category:Golden ratio]]
[[Category:Magic symbols]]
[[Category:National symbols of Ethiopia]]
[[Category:National symbols of Morocco]]
[[Category:5 (number)]]
[[Category:Pythagorean symbols]]
[[Category:Religious symbols]]
[[Category:Star polygons|05]]
[[Category:Serer religious symbols]]
[[Category:Wicca]]
[[Category:Paganism]]