Heptagram

Heptagram

A heptagram or septegram is a seven-pointed star drawn with seven straight strokes.

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

Former Georgian coat of arms, 1918–1921, 1991–2004

Flag of Cherokee Nation

The seven-pointed star of the Felibritge on the national Occitan flag.

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.
• The second heptagram is known among Pagans as the Elven Star or Fairy Star, a sacred symbol to those who follow the Faery tradition and Faeids faith. 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 simply as a septegram. The second heptagram is also a symbol of magical power in other Pagan religions. The {7/3} heptagram is also underlying the weekday heptagram.
• The heptagram is also used in Christianity to symbolize the seven days of creation and became a traditional symbol for warding off evil.^{[citation needed]}
• 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.
• In the Philosophy of Equalization a seven-sided star can refer to the seven elements of the universe.

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.

Modern:

• The rock band Tool has been known to use an irregular heptagram star on-stage and as part of their ToolArmy logo.
• The artist/band Marilyn Manson has used the heptagram in several of his logos and on the official Marilyn Manson message boards.
• The logo of the shipping company Mærsk is a white heptagram on a light blue background.
• Delta Tau Delta fraternity incorporates a seven-pointed star into its symbols.
• The California Highway Patrol uses a seven-pointed star in its insignias and badges. The specific shape varies somewhat; the badge shape is close to a regular heptagram.
• The Polish black metal band Behemoth uses a heptagram as its symbol.

See also

• Star (polygon)
• Stellated polygons
• Two-dimensional regular polytopes

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.

External links

• Weisstein, Eric W., "Heptagram" from MathWorld.
• Approximate construction method