An npointed magic star is a star polygon with Schläfli symbol {n/2}^{[1]} in which numbers are placed at each of the n vertices and n intersections, such that the four numbers on each line sum to the same magic constant.^{[2]} A normal magic star contains the consecutive integers 1 to 2n. No numbers are ever repeated.^{[3]} The magic constant of an npointed normal magic star is M = 4n + 2.
No star polygons with fewer than 5 points exist, and the construction of a normal 5pointed magic star turns out to be impossible. It can be proven that there exists no 4pointed star that will satisfy the conditions here. The smallest examples of normal magic stars are therefore 6pointed. Some examples are given below. Notice that for specific values of n, the npointed magic stars are also known as magic hexagram etc.
Magic hexagram M = 26 
Magic heptagram M = 30 
Magic octagram M = 34 
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MAGIC STAR TRAVELLER

How to Make a Magic Star  Origami  Christmas Star
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See also
References
 ^ Weisstein, Eric W. "Star Polygon". MathWorld.
 ^ Staszkow, Ronald (20030501). Math Skills: Arithmetic with Introductory Algebra and Geometry. Kendall Hunt. ISBN 9780787292966.
 ^ "Magic Stars Index Page". www.magicsquares.net. Retrieved 20170114.