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{{Short description|Five-pointed star polygon}}
[[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|star polygon]], formed from the diagonal [[Line segment|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 [[Religion:Wicca|Wicca]]ns and in [[Religion:Paganism|paganism]], or as a sign of life and connections. The word "pentagram" refers only to the five-pointed star, not the surrounding circle of a pentacle.

Pentagrams were used symbolically in {{wipe|Ancient Greece}} and [[History:Babylonia|Babylonia]]. Christians once commonly used the pentagram to represent the [[Religion:Five Holy Wounds|five wounds of Jesus]].  

The word ''pentagram'' comes from the [[Social: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 [[Religion:Marduk|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 the left-handed version.]]

Pentagram symbols from about 5,000 years ago were found in the Liangzhu culture of {{wipe|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>

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> [[Philosophy:Pythagoreanism|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>

The word ''Pentemychos'' ({{lang|grc|πεντέμυχος}} lit. "five corners" or "five recesses")<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Dpente%2Fmuxos πεντέμυχος], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus</ref> was the title of the [[Astronomy:Cosmogony|cosmogony]] of  [[Biography:Pherecydes of Syros|Pherecydes of Syros]].<ref>This is a lost book, but its contents are preserved in [[Biography:Damascius|Damascius]], ''De principiis'', quoted in Kirk and Raven, (1983) [1956], p. 55.</ref>
Here, the "five corners" are where the seeds of [[Religion:Chronos|Chronos]] are placed within the Earth in order for the [[Astronomy:Cosmos|cosmos]] to appear.<ref name="Kirk and Raven">"the divine products of [[Religion:Chronos|Chronos]]' seed, when disposed in five recesses, were called πεντέμυχος (Pentemychos)" {{cite book |first1=Geoffrey Stephen |last1=Kirk |first2=John Earle |last2=Raven |first3=Malcolm |last3=Schofield |date=1983 |orig-year=1957 |title=The Presocratic Philosophers: A Critical History with a Selection of Texts |edition=2nd, illustrated, revised, reprint |publisher=Cambridge University Press |isbn= 978-0-521-27455-5 |pages=51–52, 55 |url=https://books.google.com/books?id=kFpd86J8PLsC&pg=PA52 |quote=the only other place in [[Biography:Homer|Homer]] where Ortygie {{sic}} is mentioned is ''[[Religion:Odyssey|Odyssey]]'' V, 123, where [[Unsolved:Orion (mythology)|Orion]], having been carried off by Eos [the dawn], is slain... by [[Religion:Artemis|Artemis]]... since solstices would normally be observed at sunrise in summer, and so in the north-east-by-east direction, that is what the phrase might suggest... the dwelling-place of Eos... [[Place:Colchis|''Aia'']]..}}</ref>{{clarify|date=December 2018|reason=not clear if this was specifically a star pentagon}}

In [[Philosophy:Neoplatonism|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|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 [[Biography:Iamblichus|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>

===Western symbolism===
====Middle Ages====
The pentagram was used in ancient times as a Christian symbol for the five [[Philosophy:Sense|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 [[Religion: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 unnamed poet credits the symbol's origin to King [[Biography:Solomon|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 had of Jesus, and exemplifies the five virtues of knighthood,<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.

====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=Weiser |location=York Beach |first=Éliphas |last=Lévi |others=Trans. by [[Biography:A. E. Waite|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 [[Unsolved:Black magic|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=Weiser |location=Boston |first=Éliphas |last=Lévi |others=Trans. by [[Biography:Aleister Crowley|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 |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 ''[[Unsolved: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 [[Philosophy:Occult|occult]]ist and magician Éliphas Lévi's pentagram, which he considered to be a symbol of the [[Philosophy: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'' (1808), where a pentagram prevents [[Unsolved:Mephistopheles|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:<ref>{{cite book|first=Jón |last=Árnason |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 something else; 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. -->

===East Asian symbolism===
{{off topic|date=May 2023}}<!--the fact that there are five elements in China on its own has nothing to do with the topic "Pentagram". Show us evidence of the actual pentagram shape in  Chinese tradition.-->
[[File:Wuxing en.svg|thumb|upright|Wu Xing's five phases]]
[[Philosophy:Wuxing (Chinese philosophy)|Wu Xing]] ({{zh|c=五行|p=Wǔ Xíng}}) are the five phases, or five elements in [[Philosophy:Taoism|Taoist]] Chinese tradition. They are differentiated  from the formative ancient [[Philosophy:Godai (Japanese philosophy)|Japanese]] or [[Philosophy:Classical element|Greek elements]], due to their emphasis on cyclic transformations and change. The five phases are: Fire (火 ''huǒ''), Earth (土 ''tǔ''), Metal (金 ''jīn''), Water (水 ''shuǐ''), and Wood (木 ''mù''). The Wuxing is the fundamental philosophy and doctrine of [[Medicine:Traditional Chinese medicine|traditional Chinese Medicine]] and [[Unsolved:Acupuncture|Acupuncture]].<ref>{{Cite journal|last=Chen|first=Yuan Julian|title=Legitimation Discourse and the Theory of the Five Elements in Imperial China |url=https://www.academia.edu/23276848 |journal=Journal of Song-Yuan Studies |year=2014 |volume=44 |issue=1 |pages=325–364 |doi=10.1353/sys.2014.0000 |s2cid=147099574 |language=en}}</ref>

===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.

[[Biography:Aleister Crowley|Aleister Crowley]] made use of the pentagram in his Thelemic system of magick: 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 [[Philosophy:Evil|evil]] and associated it with the triumph of matter over spirit.

===Use in new religious movements===

====Baháʼí Faith====
[[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 [[Social:Baháʼí Faith|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'' ({{lang-ar|"temple"}}), and it was initiated and established by the [[Biography:Báb|Báb]]. The Báb and [[Biography:Bahá'u'lláh|Bahá'u'lláh]] wrote various works in the form of a pentagram.<ref name="Momen">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 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 [[Religion: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 |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=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 right to 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 [[Religion:Wicca|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.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 [[Religion:Satanism|Satanism]].
| image2            = Baphomet Pentagram.svg
| caption2          = The [[Religion:Sigil of Baphomet|Sigil of Baphomet]], insignia of the [[Religion:Church of Satan|Church of Satan]] and [[Philosophy:LaVeyan Satanism|LaVeyan Satanism]]
}}

The inverted pentagram is broadly used in [[Religion:Satanism|Satanism]], sometimes depicted with the goat's head of [[Unsolved:Baphomet|Baphomet]], as popularized by the [[Religion:Church of Satan|Church of Satan]] since 1968. Other depictions of the Satanic goat's head resemble the pentagram lacking explicit outlines. The [[Religion:Sigil of Baphomet|Sigil of Baphomet]] was adapted for the [[Organization:Joy of Satan Ministries|Joy of Satan Ministries]] logo, using [[Social:Cuneiform|cuneiform]] character at the five points of the pentagram, reflecting the shape's earliest use in Sumeria. The inverted pentagram also appears in [[Religion:The Satanic Temple|The Satanic Temple]] logo, with an alternate depiction of Baphomet's head.

====Serer religion====
The five-pointed star is a symbol of the Serer religion and the Serer people of West Africa. Called ''Yoonir'' in their language, it symbolizes the universe in the [[Religion:Serer creation myth|Serer creation myth]], and also represents the star [[Astronomy:Sirius|Sirius]].{{sfn|Gravrand|1990|p=20}}<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 |pages=27, 155 |date=1996 |isbn=0-660-15965-1}}</ref>

==== Judaism ====
The pentagram has been used in [[Religion:Judaism|Judaism]] since at least 300 BCE when it first was used as the stamp of [[Place:Jerusalem|Jerusalem]]. It is used to represent justice, mercy, and wisdom.

===Other modern use===
*The pentagram is featured on the national flags of Morocco (adopted 1915) and 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|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 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 {{wipe|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|Koch snowflake]]s drawn with [[MSWLogo|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>) ]]
The pentagram is the simplest [[Regular polygon|regular]] [[Star polygon|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|symmetry group]] the [[Dihedral group|dihedral group]] of order 10.

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

===Construction===
The pentagram can be constructed by connecting alternate vertices of a [[Pentagon|pentagon]]; see [[Pentagon#Construction of a regular pentagon|details of the construction]]. It can also be constructed as a [[Stellation|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|golden ratio]] to one another.]]
The [[Golden ratio|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|isosceles triangle]]s: five acute and five 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|star polygon]] on a sphere, composed of five great circle arcs, whose all internal angles are right angles. This shape was described by [[Biography:John Napier|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 [[Biography:Carl Friedrich Gauss|Carl Friedrich Gauss]].

===Three-dimensional figures===
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|5-cell]] (4-[[Simplex|simplex]]) has five vertices and 10 edges.
|[[File:4-simplex t1.svg|180px]]<br />The [[Rectified 5-cell|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|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 [[Astronomy:Planet|planet]] [[Astronomy:Venus|Venus]] as observed from [[Astronomy:Earth|Earth]]. Successive [[Astronomy:Conjunction#Superior and inferior|inferior conjunction]]s of Venus repeat with an orbital resonance of approximately 13:8—that is, Venus orbits the [[Astronomy:Sun|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 |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|intersection]]s [[Equidistant|equidistant]] from the figure's center have the same geometric relationship.

==In computer systems==
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|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}}

==Bibliography==
* {{cite book |chapter=Pentagram |title=The Continuum Encyclopedia of Symbols |publisher=Continuum Books |location=New York City |first=Udo |last=Becker |translator-first=Lance W. |translator-last=Garmer |page=[https://archive.org/details/continuumencyclo00beck/page/230 230] |date=1994 |isbn=978-0-8264-0644-6 |chapter-url=https://archive.org/details/continuumencyclo00beck/page/230 }}
* {{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 |first2=Heidi |last2=Burgiel |first3=Chaim |last3=Goodman-Strauss |page=404 |date=April 2008 |isbn=978-1-56881-220-5 }}
* {{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 }}
* {{Cite book |title=La civilisation Sereer, Volume II: Pangool |series=Nouvelles éditions Africaines du Sénégal |location=Dakar, Senegal |language=fr |first=Henry |last=Gravrand |date=January 1990 |isbn=2-7236-1055-1 }}
* {{cite book |title=Tilings and Patterns |publisher=W. H. Freeman |location=New York |first1=Branko |last1=Grünbaum |first2=Geoffrey Colin |last2=Shephard |date=1987 |isbn=978-0-7167-1193-3 |url=https://archive.org/details/isbn_0716711931 }}
* {{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 |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 }}

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

{{Polygons}}

[[Category:Christian symbols]]
[[Category:Golden ratio]]
[[Category:5 (number)]]
[[Category:Star polygons|05]]

{{Sourceattribution|Pentagram}}