Pentagram

pentagrams{5/2}five-pointed starpentaclePentagram of VenusPentangles5-pointed star5/2five pointed starfive-pointed stars
A pentagram (sometimes known as a pentalpha, pentangle or star pentagon) is the shape of a five-pointed star.wikipedia
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Wicca

WiccanWiccansEclectic Wicca
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 the Jews.
The five elements are symbolised by the five points of the pentagram, the most prominently used symbol of Wicca.

Pythagoreanism

PythagoreanPythagoreansPythagorean school
In Neoplatonism, the pentagram was said to have been used as a symbol or sign of recognition by the Pythagoreans, who called the pentagram ὑγιεία hugieia "health"
They also revered the pentagram, as each diagonal divides the two others at the golden ratio.

Pentacle

pentacle to SatanpentaclesWiccan pentacle
The word "pentacle" is sometimes used synonymously with "pentagram".
For example, the Online Oxford English Dictionary (2007 revision) states that the words 'pentacle' and 'pentagram' (a five-point unicursal star) are essentially synonymous.

Lesser banishing ritual of the pentagram

Lesser ritual of the pentagramLBRPPentagram
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.
The ritual is perceived as banishing any "chaotic" and "impure" forms of the elements from the magician's circle tracing the Pentagrams in the air and by the power of certain Divine names followed by an invocation of the spiritual forces ruling the elements to fortify and guard the circle.

Flag of Morocco

MoroccoFlagFlag of
*The pentagram is featured on the national flags of Morocco (adopted 1915) and Ethiopia (adopted 1996 and readopted 2009)
The flag of Morocco is made a red field with a black-bordered green pentagram.

Schläfli symbol

Schläfliextended Schläfli symbolSchläflisymbol
It is represented by the Schläfli symbol {5/2}.
For example, {5/2} is a pentagram.

Éliphas Lévi

Eliphas LeviEliphas LéviAlphonse Louis Constant
He was also the first to declare that a pentagram or five-pointed star with one point down and two points up represents evil, while a pentagram with one point up and two points down represents good.

Star polygon

starstarsStar (polygon)
The pentagram is the simplest regular star polygon.
The first usage is included in polygrams which includes polygons like the pentagram but also compound figures like the hexagram.

Drude

DrudenDrudenfusstrute
The apotropaic use of the pentagram symbol in German folklore (called Drudenfuss in German) is referred to by Goethe in 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):
The Drudenfuss (or Drudenfuß), literally "drude's foot" (also Alpfuss ), is the pentagram symbol (in early usage also either a pentagram or a hexagram), believed to ward off demons, explicitly so named in Goethe's Faust (1808).

Pentagon

{5}pentagonalpentagons
The pentagram can be constructed by connecting alternate vertices of a pentagon; see details of the construction.
A self-intersecting regular pentagon (or star pentagon) is called a pentagram.

Golden ratio

golden sectiongolden meanφ
The golden ratio, φ = (1 + √5) / 2 ≈ 1.618, satisfying
Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry; the division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams and pentagons.

Stellation

stellatedStellated polygonsstellated polyhedra
It can also be constructed as a stellation of a pentagon, by extending the edges of a pentagon until the lines intersect.

Five-pointed star

five-pointedstarstars
If the collinear edges are joined together a pentagram is produced.

Seal of Solomon

Ring of SolomonSolomon's sealGreat Seal
It was often depicted in either a pentagram or hexagram shape; the latter also known as the Star of David in Jewish tradition.

Truncation (geometry)

truncatedtruncationtruncations
A uniform truncated pentagram t{5/2} produces a doubly-wrapped pentagon with overlapping vertices and edges, {10/2}.
A truncated pentagram {5/2} will look like a pentagon, but is actually a double-covered (degenerate) decagon ({10/2}) with two sets of overlapping vertices and edges.

Golden triangle (mathematics)

golden trianglegolden gnomonRobinson triangles
The acute triangles are golden triangles.
Also, it is the shape of the triangles found in the points of regular pentagrams.

Pentagram map

The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections.

Hexagram

hexagramsAltered hexagonHexagram''' (shape)
It was first used as a religious symbol by Arabs in the medieval period, known as the Seal of Solomon, depicted as either a hexagram or pentagram, and which was later adopted by Jewish Kabbalists.

Heptagram

{7/2}seven pointed starseven-pointed star
The smallest star polygon is the {5/2} pentagram.

Pentagonal pyramid

J 2 5
It can be seen as a net of a pentagonal pyramid although with isosceles triangles.
The pentagrammic star pyramid has the same vertex arrangement, but connected onto a pentagram base:

Star polygons in art and culture

six-pointed stareight-pointed starsix-pointed stars
If the colinear edges are joined together, a pentagram is produced, which is the simplest of the unicursal star polygons, and a symbol of mystical and magical significance.

Lute of Pythagoras

The lute of Pythagoras is a self-similar geometric figure made from a sequence of pentagrams.

Regular polygon

regularregular polygons30-gon
The pentagram is the simplest regular star polygon.
The most common example is the pentagram, which has the same vertices as a pentagon, but connects alternating vertices.

Venus

Morning Starevening starplanet Venus
The pentagram of Venus is the apparent path of the planet Venus as observed from Earth.
The pentagram of Venus is the path that Venus makes as observed from Earth.