# Heptagram

Last updated
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, septegram or septogram is a seven-point star drawn with seven straight strokes.

## Contents

The name heptagram combines a numeral prefix, hepta- , with the Greek suffix -gram . The -gram suffix derives from γραμμῆ (grammē) 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 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

### 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 symbol is used in some Christian branches such as Catholicism and Orthodox Christianity.
• The symbol is also used in Kabbalist Judaism.
• In Islam, the heptagram is used to represent the first seven verses in the Quran.
• 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 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 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. [2] [3]
• 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.
• 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, The Tool Army. It is ‘open’ to signify an invitation into the collective unconscious.

## Related Research Articles

In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in n dimensions to form a new figure. Starting with an original figure, the process extends specific elements such as its edges or face planes, usually in a symmetrical way, until they meet each other again to form the closed boundary of a new figure. The new figure is a stellation of the original. The word stellation comes from the Latin stellātus, "starred", which in turn comes from Latin stella, "star".

A pentagram is the shape of a five-pointed star polygon.

A hexagram (Greek) or sexagram (Latin) is a six-pointed geometric star figure with the Schläfli symbol {6/2}, 2{3}, or {{3}}. Since there are no true regular continuous hexagrams, the term is instead used to refer to a compound figure of two equilateral triangles. The intersection is a regular hexagon.

In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, however certain notable ones can arise through truncation operations on regular simple and star polygons.

A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that the faces are congruent regular polygons which are assembled in the same way around each vertex.

In Euclidean geometry, a regular polygon is a polygon that is equiangular and equilateral. Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon, if the edge length is fixed.

In geometry, a heptagon is a seven-sided polygon or 7-gon.

In geometry, the Schläfli symbol is a notation of the form that defines regular polytopes and tessellations.

In geometry, an octagram is an eight-angled star polygon.

In geometry, a truncation is an operation in any dimension that cuts polytope vertices, creating a new facet in place of each vertex. The term originates from Kepler's names for the Archimedean solids.

Star polygons and polygonal compounds are the basis for numerous figures of significance in arts and culture. The figure may be the border or interior of the polygon, or one or more closed polygonal paths that include all of the border and also have some legs crossing the interior. Impressions of astronomical stars provide the term, but specific uses may exploit the connection or not. Stars often represent the unity of states within a country when they are used as a part of the flag.

In geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon.

In geometry, a decagram is a 10-point star polygon. There is one regular decagram, containing the vertices of a regular decagon, but connected by every third point. Its Schläfli symbol is {10/3}.

A dodecagram is a star polygon or compound with 12 vertices. There is one regular dodecagram polygon, {12/5}, having a turning number of 5. There are also 4 regular compounds {12/2}, {12/3} {12/4}, and {12/6}

In geometry, an enneagram is a nine-pointed plane figure. It is sometimes called a nonagram or nonangle.

In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but can also include disconnected sets of edges, called a compound polygon. For example, a regular pentagram, {5/2}, has 5 sides, and the regular hexagram, {6/2} or 2{3}, has 6 sides divided into two triangles.

## 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)