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Six-pointed star polygon / From Wikipedia, the free encyclopedia

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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.

Quick facts: Regular hexagram, Type, Edges and vertices, S...
Regular hexagram
A regular hexagram
TypeRegular polygonal figure
Edges and vertices6
Schläfli symbola{6}, {6/2}, 2{3} or {{3}}
Coxeter–Dynkin diagramsCDel_node_h3.pngCDel_6.pngCDel_node.png or CDel_node_h3.pngCDel_3.pngCDel_node_h3.png
Symmetry groupDihedral (D6)
Internal angle (degrees)60°
Propertiesstar, compound, cyclic, equilateral, isogonal, isotoxal
Dual polygonself
A regular hexagram, {6}[2{3}]{6}, can be seen as a compound composed of an upwards (blue here) and downwards (pink) facing equilateral triangle, with their intersection as a regular hexagon (in green).

The hexagram is part of an infinite series of shapes which are compounds of two n-dimensional simplices. In three dimensions, the analogous compound is the stellated octahedron, and in four dimensions the compound of two 5-cells is obtained.

It has been historically used in various religious and cultural contexts and as decorative motifs. The symbol was used as a decorative motif in medieval Christian churches and Jewish synagogues.[1] The hexagram is thought to have originated in Buddhism and was also used by Hindus. It was used by Muslims as a mystic symbol in the medieval period, known as the Seal of Solomon, depicted as either a hexagram or pentagram. [2][3]

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