Heptagram

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Regular heptagram (7/2)
Regular star polygon 7-2.svg
A regular heptagram
Type Regular star 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 star 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, 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}.

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


Uses

Flags and heraldry

Law enforcement

Religious and occult symbolism

Seal of Babalon and the A[?]A[?] Babalon seal.png
Seal of Babalon and the A∴A∴
Logo of Maersk Maersk Group Logo.svg
Logo of Maersk

See also

Related Research Articles

Stellation

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".

Pentagram Shape of a five-pointed star

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

Hexagram Six-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.

Star polygon

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.

Heptagon shape with seven sides

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

Schläfli symbol Notation that defines regular polytopes and tessellations

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

Octagram star polygon

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

Truncation (geometry)

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.

Tetradecagon Polygon with 14 edges

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

Decagram (geometry) 10-pointed star 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}.

Dodecagram star polygon

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}

Enneagram (geometry) star polygon

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

Polygram (geometry) Mathematical term in geometry

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

Bibliography