an n-pointed magic star is a star polygon with schlÃ¤fli symbol {n/2} 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. a normal magic star contains the consecutive integers 1 to 2n. no numbers are ever repeated. the magic constant of an n-pointed normal magic star is m&nbsp;=&nbsp;4n&nbsp;+&nbsp;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. {| style="margin:auto" |- valign="bottom" | style="padding: 0 1em" | file:magic6star-sum26.svg | style="padding: 0 1em" | file:magic7star-sum30.svg | style="padding: 0 1em" | file:magic8star-sum34.svg |- | align="center" | magic hexagramm = 26 | align="center" | magic heptagramm = 30 | align="center" | magic octagramm = 34 |} ==see also== *magic square ==external links== *marian trenkler's magic stars *gianni sarcone's magic star
Magic_squares Star_symbols