Hexagram
The hexagram is the star polygon 
, 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 
(red circle),
the inradius (green circle) is
 |
(1)
|
and the circle passing through the intersections of the triangles has radius
 |
(2)
|
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 
, the areas of the intersection and union
of the two constituent triangles are
 |  |  |
(3)
|
 |  |  |
(4)
|
There is a "nonregular" hexagram that can be obtained by spacing the integers 1 to 6 evenly around a circle and connecting 
.
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 
to 
(mod 6) and
some edges going from 
to 
(mod 6). However,
it is connected, since there is a path from any 
to any 
.
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hexagram
