# Heptagram

Regular heptagram (7/2)

A regular heptagram
Type Regular star polygon
Edges and vertices 7
Schläfli symbol {7/2}
Coxeter diagram
Symmetry group Dihedral (D7)
Internal angle (degrees) ≈77.143°
Dual polygon self
Properties star, cyclic, equilateral, isogonal, isotoxal
Regular heptagram (7/3)

A regular heptagram
Type Regular star polygon
Edges and vertices 7
Schläfli symbol {7/3}
Coxeter diagram
Symmetry group Dihedral (D7)
Internal angle (degrees) ≈25.714°
Dual polygon self
Properties star, cyclic, equilateral, isogonal, isotoxal

A heptagram, septagram, or septegram 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 γραμμῆς (grammēs) meaning a line.[1]

## 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, 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

## In popular culture

### Religious and occult symbolism

• The heptagram was used in Christianity to symbolize the seven days of creation and became a traditional symbol for warding off evil.
• The heptagram is a symbol of perfection (or God) in many Christian sects.
• The heptagram is used in the symbol for Babalon in 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 religions.
• The {7/3} heptagram is used by some members of the otherkin subculture as an identifier.
• In alchemy, a seven-sided star can refer to the seven planets which were known to ancient alchemists.

### Other

• A seven pointed star is used as the badge in many sheriff's departments and some smaller-community police departments.
• 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.

## References

1. γραμμή, Henry George Liddell, Robert Scott, A Greek-English Lexicon, on Perseus

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-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 26. pp. 404: Regular star-polytopes Dimension 2)