# Heptagram

A heptagram, septagram, septegram or septogram is a seven-point star drawn with seven straight strokes.
The name heptagram combines a numeral prefix, hepta-, with the Greek suffix -gram. The -gram suffix derives from γραμμῆ (grammē) meaning a line.

## 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 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}.
| {7/2} | {7/3} | {7}+{7/2}+{7/3} |
| 7-2 prism | 7-3 prism | Complete graph |
| 7-2 antiprism | 7-3 antiprism | 7-4 antiprism |

## Uses
### Flags and heraldry

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

### Law enforcement

* Seal of the California Highway Patrol

### Religious and occult symbolism

* The heptagram became a traditional symbol for warding off evil in Catholicism.
* The symbol is also used in Kabbalist Judaism.
* 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 Star or Fairy 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.
* In alchemy, 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 astrology. For example, the planetary hours, from which comes the names of the days of the week.
* 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.
* 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.

### In popular culture

* 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.
* In George 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".

### Variants

* Interlaced; equivalent to the 7$_1$ knot