# Hexagram

six-pointed star polygon

A hexagram is a six-pointed star, with all lines the same length and all angles the same. A 'hexangle', 'star hexagon', or 'hexalpha' means the same thing.[1] It is used in historical, religious and cultural contexts, for example in Hanafism,[2] Judaism, Hinduism and occultism. It is possible that this simple geometric shape, like the triangle, circle, or square, has been created by various peoples with no connection to one another.

## Group theory

In mathematics, the root system for the simple Lie group G2 is in the form of a hexagram, with six long roots and six short roots.

## Construction by compass and a straight edge

A six-pointed star, like a regular hexagon, can be created using a compass and a straight edge:

• Make a circle of any size with the compass.
• Without changing the radius of the compass, set its pivot on the circle's circumference, and find one of the two points where a new circle would intersect the first circle.
• With the pivot on the last point found, similarly find a third point on the circumference, and repeat until six such points have been marked.
• With a straight edge, join alternate points on the circumference to form two overlapping equilateral triangles.

## References

1. Graham, Dr. O.J. 2001. The Six-Pointed Star: its origin and usage. 4th ed, Toronto: The Free Press, . ISBN 0-9689383-0-2
2. Miller, Sam 2010. Delhi: Adventures in a Megacity, page 91.