TOPICS
Search

Hexagram


Hexagram

The hexagram is the star polygon {6/2}, also known as the star of David or Solomon's seal, illustrated at left above.

It appears as one of the clues in the novel The Da Vinci Code (Brown 2003, p. 455).

For a hexagram with circumradius R=a (red circle), the inradius (green circle) is

 r=1/2a
(1)

and the circle passing through the intersections of the triangles has radius

 rho=1/3sqrt(3)a.
(2)
HexagramAreas

The interior of a hexagram is a regular hexagon with side lengths equal to 1/3 that of the original hexagram. Given a hexagram with line segments of length a, the areas of the intersection and union of the two constituent triangles are

A_1=1/6sqrt(3)
(3)
A_2=1/3sqrt(3).
(4)
UnicursalHexagram

There is a "nonregular" hexagram that can be obtained by spacing the integers 1 to 6 evenly around a circle and connecting 0->3->5->1->4->2->0. The resulting figure is called a "unicursal hexagram" and was evidently discovered in the 19th century. It is not regular because there are some edges going from k to k+2 (mod 6) and some edges going from k to k+3 (mod 6). However, it is connected, since there is a path from any i to any j.


See also

Chinese Checkers, Dissection, Magic Hexagram, Pentagram, Polygram, Solomon's Seal Knot, Star Figure, Star of Lakshmi, Star Number, Unicursal Circuit

Portions of this entry contributed by Chris Heckman

Explore with Wolfram|Alpha

References

Brown, D. The Da Vinci Code. New York: Doubleday, 2003.

Cite this as:

Heckman, Chris and Weisstein, Eric W. "Hexagram." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Hexagram.html

Subject classifications