Magic star

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An n-pointed 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 n-pointed normal magic star is M = 4n + 2.


No star polygons with fewer than 5 points exist, and the construction of a normal 5-pointed magic star turns out to be impossible. It can be proven that there exists no 4-pointed star that will satisfy the conditions here. The smallest examples of normal magic stars are therefore 6-pointed. Some examples are given below. Notice that for specific values of n, the n-pointed magic stars are also known as magic hexagram etc.

Magic6star-sum26.svg Magic7star-sum30.svg Magic8star-sum34.svg
Magic hexagram
M = 26
Magic heptagram
M = 30
Magic octagram
M = 34

See also

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  1. Weisstein, Eric W. "Star Polygon". MathWorld .
  2. Staszkow, Ronald (2003-05-01). Math Skills: Arithmetic with Introductory Algebra and Geometry . Kendall Hunt. p.  374. ISBN   9780787292966. magic star math.
  3. "Magic Stars Index Page". Retrieved 2017-01-14.