Heptagram

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 heptagon, {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 and its related {8/2} star figure (a compound of two squares), followed by the regular enneagram, which also has two forms: {9/2} and {9/4}, as well as one compound of three triangles {9/3}.

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  Former Georgian coat of arms, 1918–1921, 1991–2004
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  Flag of Eastern Band Cherokee
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  The seven-pointed star of the Felibritge on the Occitan flag.
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  The Jordanian flag, bearing the star that symbolizes Al-Fatiha
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  Symbol of Hokkaido
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  Coat of arms of Samarkand
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  Commonwealth Star as the crest of Coat of Arms of Australia
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  The flag of Cook County, Illinois, adopted in June 2022 and taking design cues from the Flag of Chicago, its county seat
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  The coat of arms and flag of Thun Switzerland

• The seven-pointed star is incorporated into the flags of various bands of Cherokee Indians and the badges of Navajo Nation Police (as well as other police).
• The Bennington flag, a historical American Flag, has thirteen seven-pointed stars along with the numerals "76" in the canton.
• The Flag of Jordan contains a seven-pointed star.
• 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 the Georgian Soviet Socialist Republic used the {7/2} heptagram as an element.
• A seven-pointed star is used as the badge in many sheriff's departments and some smaller-community police departments.
• A seven-pointed star is used in the otherkin pride flag.

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  Seal of the California Highway Patrol

• The heptagram became a traditional symbol for warding off evil in Catholicism.
• The symbol is also used in Kabbalist Judaism.
• InIslam, the heptagram is used to represent the first seven verses in the Quran.
• The heptagram is used in the symbol for Babalon in Aleister Crowley's occult system Thelema.
• The heptagram is known among neopagans as the Elven StarorFairy Star. It is treated as a sacred symbol in various modern pagan and witchcraft traditions. Blue Star Wicca also uses the symbol, where it is referred to as a septegram. The second heptagram is a symbol of magical power in some pagan spiritualities.
• Inalchemy, a seven-sided star can refer to the seven planets which were known to early alchemists, and also, the seven alchemical substances: fire, water, air, earth, sulphur, salt and mercury.
• In Polynesia, the seven-pointed star is used often in imagery, basket making, tattoos, and is considered to be a symbol of Kanaloa, the first Polynesian navigator.^[2][3]
• The seven-sided star is an important symbol of the Cherokee people of southern Appalachia, representing the seven clans of the Cherokee and the sacred number seven.

• The logo of American shoe brand DC Shoes features a 7/3 heptagram in the letter C.
• The seven-pointed star is used as the logo for the international Danish shipping company A.P. Moller–Maersk Group, sometimes known simply as Maersk.
• InGeorge R. R. Martin's novel series A Song of Ice and Fire and its TV version Game of Thrones, a seven-pointed star serves as the symbol of the Faith of the Seven.
• In the manga series MeruPuri, a magical mirror/ portal is in the shape of a heptagram. The symbol is also seen during spellcasting.
• Finnish rock band HIM used a heptagram on the cover of their eighth studio album Tears on Tape.
• American heavy metal band Darkest Hour used a heptagram on the cover of their eighth studio album Darkest Hour.
• English Singer Damon Albarn uses a heptagram as a symbol in his solo performances and with his band Blur.
• The {7/3} heptagram is used by some members of the otherkin subculture as an identifier.
• The American Progressive Rock Metal Band “Tool” uses an ‘open’ seven pointed symbol for their fan group. It is ‘open’ to signify an invitation into the collective unconscious.
• An alternate logo of Chicago-based Children's Press from 1945 to 1970, having the slogan "Children's Books Are Important".

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  Interlaced; equivalent to the 7₁ knot

• Grünbaum–Rigby configuration
• Star polygon
• Stellated polygons
• Two-dimensional regular polytopes
• Major (United States) insignia of seven leaves

Bibliography

• 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.
• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26. pp. 404: Regular star-polytopes Dimension 2)

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