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Regular hexagram

A regular hexagram
Type Regular polygon
Edges and vertices 6
Schläfli symbol {6/2}, 2{3} or {{3}}
Symmetry group Dihedral (D6)
Internal angle (degrees) 60°
Dual polygon self
Properties star, compound, cyclic, equilateral, isogonal, isotoxal

A hexagram (Greek) or sexagram (Latin) is a six-pointed geometric star figure with Schläfli symbol {6|2}, 2{3}, or {{3}}. It is the compound of two equilateral triangles. The intersection is a regular hexagon.

It is used in historical, religious and cultural contexts, for example in Jewish identity, Hinduism, Occultism and Islam.

## Group theory

In mathematics, the root system for the simple Lie group G2 is in the form of a hexagram.

## Origins and shape

It is possible that as a simple geometric shape, like for example the triangle, circle, or square, the hexagram has been created by various peoples with no connection to one another.

The hexagram is a mandala symbol called satkona yantra or sadkona yantra found on ancient South Indian Hindu temples. It symbolizes the nara-narayana, or perfect meditative state of balance achieved between Man and God, and if maintained, results in "moksha," or "nirvana" (release from the bounds of the earthly world and its material trappings).Template:Fix/category[citation needed]

Another theory, though apparently not very substantiated, about the origin of the shape is that it is simply 2 of the 3 letters in the name David: in its Hebrew spelling, David is transliterated as "D-V-D." In Biblical Hebrew, the letter "D" (Dalet) was written in a form like an upside-down and backwards "L," but when seen in the Greek, the letter "Delta" (Δ) is a triangle. The symbol may have been a simple family crest formed by flipping and juxtaposing the two most prominent letters in the name. The letter "W" in this case could reference the compositing operation of the two Deltas.

Some researchers have theorized that the hexagram represents the astrological chart at the time of David's birth or anointment as king. The hexagram is also known as the "King's Star" in astrological circles.

In antique papyri, pentagrams, together with stars and other signs, are frequently found on amulets bearing the Jewish names of God, and used to guard against fever and other diseases. Curiously the hexagram is not found among these signs. In the Greek Magical PapyriTemplate:Fix/category[citation needed] (Wessely, l.c. pp. 31, 112) at Paris and London there are twenty-two signs side by side, and a circle with twelve signs, but neither a pentagram nor a hexagram.

## Other hexagrams

Other hexagrams can be constructed as a continuous path.

unicursal hexagram Two uniform star-polyhedra have hexagram vertex figures One star polyhedron has hexagram faces
D2 symmetry D3 symmetry
Vertex-transitive
D3 symmetry
Edge-transitive

Great ditrigonal icosidodecahedron

Great triambic icosahedron

## References

• Grünbaum, B. and G. C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1.
• Grünbaum, B.; Polyhedra with Hollow Faces, Proc of NATO-ASI Conference on Polytopes ... etc. (Toronto 1993), ed T. Bisztriczky et al., Kluwer Academic (1994) pp. 43–70.
• Graham, Dr. O.J. The Six-Pointed Star: Its Origin and Usage 4th ed. Toronto: The Free Press 777, 2001. ISBN 0-9689383-0-2
• Wessely, l.c. pp. 31, 112