A
pentagram (sometimes known as a
pentalpha or
pentangle or, more
formally, as a
star
pentagon) is the shape of a
fivepointed star drawn with five straight
strokes. The word
pentagram comes from the
Greek word πεντάγραμμον
(
pentagrammon), a
noun form of
πεντάγραμμος (
pentagrammos) or πεντέγραμμος
(
pentegrammos), a word meaning roughly "fivelined" or
"five lines".
Pentagrams were used symbolically in
ancient Greece and
Babylonia, and are used today as a symbol of faith
by many
Wiccans, akin to the use of the
cross by Christians and the
Star of David by Jews. The pentagram has
magical associations, and many
people who practice
Neopagan faiths wear
jewelry incorporating the symbol.
Christians once more commonly used the
pentagram to represent the
five wounds of
Jesus, and it also has associations within
Freemasonry.
The word "
pentacle" is sometimes used
synonymously with "pentagram", and this usage is borne out by the
Oxford English Dictionary, although that work specifies that a
circumscription makes the shape more particularly a pentacle.
Wiccans and Neopagans often make use of this more specific
definition for a pentagram enclosed in a circle.
Early history
Sumer
The first known uses of the pentagram are found in
Mesopotamian writings dating to about 3000
BC.The
Sumerian pentagrams served as
pictograms for the word "UB," meaning "corner, angle, nook; a small
room, cavity, hole; pitfall," suggesting something very similar to
the pentemychos (see below on the Pythagorean use for what
pentemychos means). In René Labat's index system of
Sumerian hieroglyphs/
pictograms
it is shown with two points up.In the
Babylonian context, the edges of the pentagram
were probably orientations: forward, backward, left, right, and
"above". These directions also had an
astrological meaning, representing the five
planets
Jupiter,
Mercury,
Mars and
Saturn, and
Venus as the
"Queen of Heaven" (
Ishtar) above.
Pythagoreans
The
Pythagoreans called the pentagram
ὑγιεία
Hygieia ("health"; also the Greek goddess of
health,
Hygieia), and saw in the pentagram a
mathematical perfection (see
Geometry
section below).
The five vertices were also used by the medieval neopythagoreans
(whom one could argue were not pythagoreans at all) to represent
the five
classical elements:
The vertices were labeled in the letters of υγεια. The ordering
(clockwise or counterclockwise) and starting vertex varied.
The ancient Pythagorean pentagram was drawn with two points up and
represented the doctrine of
Pentemychos.
Pentemychos means
"five recesses" or "five chambers", also known as the pentagonas —
the fiveangle, and was the title of a work written by
Pythagoras's teacher and friend
Pherecydes of Syros. It was also the
"place" where the first precosmic offspring had to be put in order
for the ordered cosmos to appear.
European occultism
Heinrich Cornelius
Agrippa and others perpetuated the popularity of the pentagram
as a magic symbol, keeping the Pythagorean attributions of elements
to the five points. By the mid19th 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 writer
Eliphas Levi 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."
 "The flaming star, which, when turned upside down, is the
hierolgyphic [sic] 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 the sign of
antagonism and fatality. It is the goat of lust attacking the
heavens with its horns."
 "Let us keep the figure of the Fivepointed 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."
Image:Pentagram and human body (Agrippa).jpgMan inscribed
in a pentagram, from Heinrich
Cornelius Agrippa's De occulta philosophia libri
tres. The five signs at the pentagram's vertices are astrological.Image:Inverted pentacle.PNGAnother
pentagram from Agrippa's book. This one has the Pythagorean letters
inscribed around the circle.Image:Pentagram (Levi).jpgThe occultist and magician Eliphas Levi's pentagram, which he considered
to be a symbol of the microcosm, or human.
Religious symbolism
Christianity
The pentagram is used as a Christian symbol for the five
senses, and if the letters
S,
A,
L,
V, and
S are inscribed in the points,
it can be taken as a symbol of
health (from
Latin salus).
Medieval Christians believed it to symbolise the five wounds of
Christ. The pentagram was believed to protect against witches and
demons.
The pentagram figured in a heavily symbolic
Arthurian romance: it appears on the shield of
Sir Gawain in the 14th century poem
Sir Gawain and the
Green Knight. As the poet explains, the five points of the
star each have five meanings: they represent the five senses, the
five fingers, the five wounds of
Christ, the
five joys that
Mary had of
Jesus (the
Annunciation, the
Nativity, the
Resurrection, the
Ascension, and the
Assumption), and the five virtues of
knighthood which Gawain hopes to embody:
noble generosity, fellowship, purity, courtesy, and
compassion.
Most Christians, probably due to their misinterpretation of symbols
used by
ceremonial magicians, came
to associate it with Satanism and subsequently rejected the symbol
sometime in the twentieth century.
Mormonism
The
Church of Jesus Christ of Latterday Saints has used pentagrams
and fivepointed stars in
Temple architecture, specifically
the
Nauvoo Illinois Temple
and the
Salt Lake Temple. These
symbols derived from traditional morning star pentagrams that are
no longer commonly used in mainstream Christianity.
Judaism
The
pentagram was the official seal of the city of Jerusalem for a time. Due to the similarity of the
star shapes, it is occasionally confused with the
Star of David by those unfamiliar with the
symbols.
Neopaganism
A typical Neopagan pentagram
(circumscribed).
Many
Neopagans, especially
Wiccans, use the pentagram as a symbol of faith
similar to the
Christian cross or the
Jewish Star of David. It is not, however, a universal
symbol for Neopaganism, and is rarely used by
Reconstructionists. Its
religious symbolism is commonly explained by reference to the
neoPythagorean understanding that the five vertices of the
pentagram represent the four
elements with the addition of Spirit as
the uppermost point. As a representation of the elements, the
pentagram is involved in the Wiccan practice of summoning the
elemental spirits of the four directions
at the beginning of a ritual.
The outer circle of the circumscribed pentagram is sometimes
interpreted as binding the elements together or bringing them into
harmony with each other. The Neopagan pentagram is generally
displayed with one point up, partly because of the "inverted"
goat's head pentagram's association with Satanism; however, within
traditional forms of
Wicca a pentagram with
two points up is associated with the Second Degree
Initiation and in this context has no relation to
Satanism.
Because of a perceived association with Satanism and also because
of negative societal attitudes towards Neopagan religions and the
"
occult", many United States schools have
sought to prevent students from displaying the pentagram on
clothing or jewelry. In public schools, such actions by
administrators have been determined to be in violation of students'
First
Amendment right to
free exercise of
religion.
Satanism
Satanists use a pentagram with two points
up, often inscribed in a double circle, with the head of a goat
inside the pentagram. This is referred to as the
Sigil of Baphomet. They use it much the
same way as the Pythagoreans, as Tartaros literally translates from
Greek as a "Pit" or "Void" in Christian terminology (the word is
used as such in the Bible, referring to the place where the
fallen angels are fettered). The
Pythagorean Greek letters are most often replaced by the
Hebrew letters לויתן forming the name
Leviathan. Less esoteric
LaVeyan Satanists use it as a sign of
rebellion or religious identification, the three downward points
symbolising rejection of the holy
Trinity.
Thelema
Aleister Crowley also made use of
the pentagram and 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. 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.
Bahá'í Faith
The pentagram is the official symbol of the
Bahá'í Faith. In the Bahá'í Faith,
the pentagram is known as the
Haykal ( ), and it
was initiated and established by the
Báb.
Both Báb and
Bahá'u'lláh wrote
various works in the form of a pentagram.
Image:HaykalBab2.gifAn unidentified work of the Báb.Image:Haykal2.gifAn unidentified work of the
Báb.
Taoism
Representation of the Chinese five
elements (Wǔ Xíng)
Taoism conceived of a five element system which governed the
natural world which they called the Wu Xing(Chinese:五行/Wǔ Xíng).
Unlike the Greek system of four elements being Earth, Air, Fire,
and Water, the Chinese system involved Fire(火/huǒ), Earth(土/tǔ),
Metal(金/jīn), Water(水/shuǐ), and Wood(木/mù). This five element
system was normally depicted as a pentagram(Chinese:五星/Wǔ Xīng)
ringed by a circle. The circle was used to describe the generative
cycle where wood feeds fire, fire creates earth (ash), earth bears
metal, metal carries water, and water nourishes wood. The pentagram
describes the destructive or overcoming system where Wood parts
Earth, Earth absorbs Water, Water quenches Fire, Fire melts Metal,
Metal chops Wood, or the alternative destructive system: Wood
absorbs Water, Water rusts Metal, Metal breaks up Earth, Earth
smothers Fire, Fire burns Wood. This system informs traditional
Chinese medicine (TCM) even today. As the Wu Xing is of great
antiquity and the silk road had been open to Europe since before
the Roman Empire it is quite likely that this medical system was
imported to Europe as a misunderstood and exotic practice involving
spirits (Shen).
Political symbolism
Flags
While a solid
fivepointed star is
found on many flags, the pentagram is relatively rare.
It appears on three
national flags, those of Ethiopia, Ghana and Morocco and in some
coats of arms.
According
to Ivan Sache, on the Moroccan flags, the
pentagram represents the link between God and
the nation. It is also possible that both flags use the
pentagram as a symbol of
King Solomon
(see
Seal of Solomon), the
archetypal wise king of
Jewish,
Christian and
Muslim lore.
The Ghana pentagram refers to the hope of Ghana being the Black
Star and a shining example to the continent.
Image:Flag of Morocco.svgMorocco's
flagImage:Flag of Ethiopia.svgEthiopia's
flag
Other organizations
Order of the Eastern Star
The
Order of the Eastern
Star, a fraternal organization associated with
Freemasonry, has employed a pointdown pentagram
as its symbol, with the five
isosceles triangles of the points colored
red, blue, yellow, white and green. This is an older form of the
order's emblem and it is now more commonly depicted with the
central pentagon rotated 36° so that it is no longer strictly a
pentagram.
In literature
In the
medieval romance of
Sir Gawain and the Green
Knight, the pentagram on
Gawain's
shield is given a Christian interpretation (see
above).
In
Goethe's
Faust, the pentagram prevents
Mephistopheles from leaving a room.
 Mephistopheles:
 :I must confess, my stepping o'er
 :Thy threshold a slight hindrance doth impede;
 :The wizardfoot doth me retain.
 Faust:
 :The pentagram thy peace doth mar?
 :To me, thou son of hell, explain,
 :How earnest thou in, if this thine exit bar?
 :Could such a spirit aught ensnare?
In
H. P. Lovecraft's
Cthulhu Mythos stories, the version of
The Elder Sign devised by
August
Derleth is a warped pentagram with a flaming eye or pillar of
flame in the center. It was first described in Derleth's novel,
The Lurker at the Threshold. (This was, however, different
from the symbol that Lovecraft himself had envisaged.)
In
Dan Brown's novel
The Da Vinci Code, the pentagram
represents Venus, based on the successive inferior conjunctions of
Venus against the
Zodiac.
In
Japanese culture, the pentagram (五芒星 gobōsei) is a
symbol of magical power, associated with the onmyoji Abe no Seimei;
it is a diagram of the "overcoming cycle" of the five Chinese elements. As a predominantly
nonChristian country, with a different set of associations
attached to the symbol, there is no social stigma associated with
it.
Geometry
The pentagram is the simplest
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.
Construction
The pentagram can be constructed by connecting alternate vertices
of a
pentagon; see
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
The
golden ratio, φ = (1+√5)/2 ≈ 1.618,
satisfying
 \varphi=1+2\sin(\pi/10)=1+2\sin 18^\circ\,
 \varphi=1/(2\sin(\pi/10))=1/(2\sin 18^\circ)\,
 \varphi=2\cos(\pi/5)=2\cos 36^\circ\,
plays an important role in regular pentagons and pentagrams. Each
intersection of edges sections the edges in 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 2
intersecting edges (a side of the pentagon in the pentagram's
center) is φ. As the fourcolor illustration shows:
 \frac{\mathrm{red}}{\mathrm{green}} =
\frac{\mathrm{green}}{\mathrm{blue}} =
\frac{\mathrm{blue}}{\mathrm{magenta}} = \varphi .
The pentagram includes ten
isosceles
triangles: 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. The obtuse isosceles triangle highlighted via the
colored lines in the illustration is a
golden gnomon.
Trigonometric values
 :See Exact
trigonometric constants: Pentagon
 \sin \frac{\pi}{10} = \sin 18^\circ = \frac{\sqrt 5 
1}{4}=\frac{\varphi1}{2}=\frac{1}{2\varphi}
 \cos \frac{\pi}{10} = \cos 18^\circ = \frac{\sqrt{2(5 + \sqrt
5)}}{4}
 \tan \frac{\pi}{10} = \tan 18^\circ = \frac{\sqrt{5(5  2 \sqrt
5)}}{5}
 \cot \frac{\pi}{10} = \cot 18^\circ = \sqrt{5 + 2 \sqrt 5}
 \sin \frac{\pi}{5} = \sin 36^\circ = \frac{\sqrt{2(5  \sqrt
5)} }{4}
 \cos \frac{\pi}{5} = \cos 36^\circ = \frac{\sqrt 5+1}{4} =
\frac{\varphi}{2}
 \tan \frac{\pi}{5} = \tan 36^\circ = \sqrt{5  2\sqrt 5}
 \cot \frac{\pi}{5} = \cot 36^\circ = \frac{ \sqrt{5(5 + 2\sqrt
5)}}{5}
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.
Threedimensional figures
 See Uniform polyhedron:
Icosahedral symmetry
Several
polyhedra incorporate
pentagrams:
Image:Pentagrammic prism.png
Pentagrammic prismImage:Pentagrammic
antiprism.png
Pentagrammic
antiprismImage:Pentagrammic crossed antiprism.png
Pentagrammic crossed
antiprismImage:Small_stellated_dodecahedron.png
Small stellated
dodecahedronImage:Small ditrigonal
icosidodecahedron.png
Small ditrigonal
icosidodecahedronImage:Small dodecahemicosahedron.png
Small
dodecahemicosahedronImage:Snub dodecadodecahedron.png
Snub
dodecadodecahedronImage:Sixteenth stellation of
icosidodecahedron.png
16th
stellation of icosidodecahedron
Higher dimensions
Orthogonal projections of higher dimensional polytopes can also
create pentagrammic figures:
All ten 4dimensional
SchläfliHess polychoron have
either pentagrammic faces or
vertex
figure elements.
In Astronomy and nature
See also
Notes
 "Pentagram" article in The Continuum Encyclopedia of
Symbols Becker, Udo, ed., Garmer, Lance W. translator, New
York: Continuum Books, 1994, p. 230.
 Signs and Symbols in Christian Art Ferguson, George,
Oxford University Press: 1966, p. 59.
 Order of the Eastern Star
 "Pentacle", Oxford English Dictionary.
 Labat, René. Manuel d'épigraphie akkadienne: Signes,
Syllabaire, Idéogrammes. The pentagram is symbol number 306 in
this system.
 http://merlinravensong2.tripod.com/thepentagram.html
 This is a lost book, but its contents are preserved in
Damascius,
De
principiis, quoted in Kirk and Raven, The PreSocratic
Philosophers, Cambridge Univ. Press, 1956, p. 55.
 Found at
http://www.scribd.com/doc/9668236/TheKeyoftheMysteriesbyLevi,
page 69.
 Christian Symbols Ancient and Modern, Child, Heather
and Dorothy Colles. New York: Charles Scribner's Sons, 1971, ISBN
0713519606.

http://www.mediade.si/media/symbolic.meaning.of.the.pentagram.extract.pdf
 Pentagram, pentacle
 Christian Symbols and How To Use Them, Knapp, Justina;
Milwaukee: The Bruce Publishing Company, 1955. Plate LXV, Plate LV
(Imprimatur, Jos. F. Busch, Bishop of St. Cloud)
 See the Nauvoo Temple website discussing its architecture, and
particularly the page on Nauvoo Temple exterior symbolism. Retrieved 13
December 2006.
 Pentagram, pentacle
 Chapter II  Second Degree Initiation
 "Religious Clothing in School", Robinson, B.A.,
Ontario Consultants on Religious Tolerance, 20 August, 1999,
updated 29 April, 2005. accessed 10 February, 2006.
 "ACLU Defends Honor Student Witch Pentacle"
press release, American Civil Liberties Union of Michigan, 10
February, 1999. accessed 10 February, 2006.
 "Witches and wardrobes: Boy says he was suspended from
school for wearing magical symbol" Rouvalis, Cristina;
Pittsburgh PostGazette, September 27, 2000. accessed 10 February,
2006.
 The Magick of Aleister Crowley p 93 and endnote 31 to
Chapter Five (p 247).
 Bahá'í Reference Library  Directives from the
Guardian, Pages 5152
 Moroccan flag on Flagspot.net accessed on 10 February,
2006.
References
 Grünbaum, B. and G. C.
Shephard; Tilings and Patterns, New York: W. H. Freeman
& Co., (1987), ISBN 0716711931.
 Grünbaum, B.; Polyhedra
with Hollow Faces, Proc of NATOASI Conference on Polytopes ...
etc. (Toronto 1993), ed T. Bisztriczky et al., Kluwer Academic
(1994) pp. 4370.
External links