Heptagram
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| Regular heptagram | |
|---|---|
 Regular {7/2} heptagram |
|
| Edges and vertices | 7 |
| Schläfli symbol | {7/2}, {7/3} |
| Coxeter diagram |      ,  |
| Symmetry group | Dihedral (D7) |
| Properties | star, cyclic, equilateral, isogonal, isotoxal |
A heptagram or septegram is a seven-pointed star drawn with seven straight strokes.
Contents |
Geometry []
In general, a heptagram is any self-intersecting heptagon (7-sided polygon).
There are two regular heptagrams, labeled as {7/2} and {7/3}, with the second number representing the vertex interval step from a regular heptagram, {7/1}.
This is the smallest star polygon that can be drawn in two forms, as irreducible fractions. The two heptagrams are sometimes called the heptagram (for {7/2}) and the great heptagram (for {7/3}).
The previous one, the regular hexagram {6/2}, is a compound of two triangles. The smallest star polygon is the {5/2} pentagram.
The next one is the {8/3} octagram, followed by the regular enneagram, which also has two forms: {9/2} and {9/4}, as well as one compound of 3 triangles {9/3}.
 First heptagram {7/2} |
 Second heptagram {7/3} |
 Both heptagrams inscribed within a heptagon |
 Heptagrammic prism (7/2) |
 Heptagrammic prism (7/3) |
In culture []
Religious/occult symbolism:
- The first heptagram was used as a symbol in the Kabbalah, and later by Aleister Crowley and the Ordo Templi Orientis where it was known as the Star (or Seal) of Babalon, featured on the seal of the A∴A∴.
- The second heptagram is known among Pagans as the Elven Star or Fairy Star. It is treated as a sacred symbol in various modern Pagan and witchcraft traditions. Similarly, it has been adopted as an identifier by some members of the Otherkin subculture. Blue Star Wicca also uses the symbol, where it is referred to as a septegram. The second heptagram is also a symbol of magical power in some Pagan religions.
- The heptagram is also used in Christianity to symbolize the seven days of creation and became a traditional symbol for warding off evil.
- The heptagram is also the symbol of perfection (or God) in many Christian religions.
- In alchemy, a seven-sided star can refer to the seven planets which were known to ancient alchemists.
Flags:
- The seven-pointed star is incorporated into the flags of the various bands of the Cherokee Nation and the badges of Navajo Nation Police (as well as other police).
- The Flag of Australia employs five heptagrams and one pentagram to depict the Southern Cross constellation and the Commonwealth Star.
- Some old versions of the Coat of arms of Georgia (country) including Soviet days had used the {7/2} heptagram as an element.
See also []
Notes []
References []
- Grünbaum, B. and G.C. Shephard; Tilings and Patterns, New York: W. H. Freeman & Co., (1987), ISBN 0-7167-1193-1 [Amazon-US | Amazon-UK].
- 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.
