Heptagram

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Regular heptagram (7/2)
Regular star polygon 7-2.svg
A regular heptagram
Type Regular polygon
Edges and vertices 7
Schläfli symbol {7/2}
Coxeter diagram CDel node 1.pngCDel 7.pngCDel rat.pngCDel 2x.pngCDel node.png
Symmetry group Dihedral (D7)
Internal angle (degrees) ≈77.143°
Dual polygon self
Properties star, cyclic, equilateral, isogonal, isotoxal
Regular heptagram (7/3)
Regular star polygon 7-3.svg
A regular heptagram
Type Regular polygon
Edges and vertices 7
Schläfli symbol {7/3}
Coxeter diagram CDel node 1.pngCDel 7.pngCDel rat.pngCDel 3x.pngCDel node.png
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-pointed 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[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
{7/2}
Acute heptagram.svg
{7/3}
Heptagrams.svg
{7}+{7/2}+{7/3}
Heptagrammic prism 7-2.png
7-2 prism
Heptagrammic prism 7-3.png
7-3 prism
6-simplex t0.svg
Complete graph
Antiprism 7-2.png
7-2 antiprism
Antiprism 7-3.png
7-3 antiprism
Antiprism 7-4.png
7-4 antiprism

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.

Flags[edit]

See also[edit]

Notes[edit]

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

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.
  • 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)

External links[edit]