Hexagram (six‑pointed star)

Form and mathematical description

Geometrically the hexagram can be seen as a compound of two equilateral triangles or as the regular star polygon with Schläfli symbol {6/2}, which links every second vertex of a hexagon. Variants include the standard two‑triangle compound and a unicursal form that is drawn with one continuous line in some symbolic traditions.

History and cultural development

Representations of six‑pointed stars occur independently in many regions and eras. The motif is found in South Asian yantras, medieval European art, Islamic architectural ornament, and other decorative traditions. In Jewish contexts the hexagram is widely known as the Star of David or Magen David and has become a modern emblem of Jewish identity. It has also been associated, in different times and places, with occult and alchemical symbolism.

Uses and meanings

• Religious and communal symbol — most famously in Judaism, but also appearing in Hindu yantras and in some Islamic decorative contexts.
• Decorative motif — tile work, architecture, textiles and heraldry employ the six‑point star for its symmetry.
• Symbolic roles — interpreted variously as union of opposites (for example upward and downward triangles), balance, or as a talisman in folk practices.
• Mathematical and pedagogical — used to illustrate symmetry, compounds of polygons, and simple star polygon constructions.

Distinctions and notable facts

It should not be confused with a hexagon (a six‑sided polygon) or with other six‑point figures formed differently. The common hexagram is a compound (two separate triangles) rather than a single unicursal star, though both forms circulate in symbolic use. Because similar designs arose independently in different cultural traditions, the hexagram’s meanings vary widely and must be read in context rather than assumed universal.

The hexagram remains a widely recognized geometric and cultural emblem, notable for its simplicity, symmetry, and versatility in both artistic design and symbolic expression.