Heptagram

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Regular heptagram
Obtuse heptagram.svg
Regular {7/2} heptagram
Edges and vertices 7
Schläfli symbol {7/2}, {7/3}
Coxeter diagram CDel node 1.pngCDel 7.pngCDel rat.pngCDel d2.pngCDel node.png, CDel node 1.pngCDel 7.pngCDel rat.pngCDel d3.pngCDel node.png
Symmetry group Dihedral (D7)
Properties star, cyclic, equilateral, isogonal, isotoxal

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

Geometry[edit]

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}.

Obtuse heptagram.svg
First heptagram {7/2}
Acute heptagram.svg
Second heptagram {7/3}
Heptagrams.svg
Both heptagrams inscribed within a heptagon
Heptagrammic prism 7-2.png
Heptagrammic prism (7/2)
Heptagrammic prism 7-3.png
Heptagrammic prism (7/3)

In culture[edit]

Religious/occult symbolism[edit]

  • 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 also the symbol of perfection (or God) in many Christian religions.
  • The heptagram is known among neo-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.
  • In alchemy, a seven-sided star can refer to the seven planets which were known to ancient alchemists.
  • In George R. R. Martin's A Song of Ice and Fire series, the dominant religion of Westeros follows The Seven, whose symbol is described as a seven-pointed star.

Flags[edit]

See also[edit]

Notes[edit]


References[edit]

  • 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[edit]