Heptagram

From Wikipedia, the free encyclopedia
Jump to: navigation, search
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 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 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 and 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 a symbol of perfection (or God) in many Christian religions.
  • 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.
  • 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]