An n-pointed magic star is a star polygon with Schläfli 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 = 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. 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.
| Magic hexagram M = 26 |
Magic heptagram M = 30 |
Magic octagram M = 34 |
Famous quotes containing the words magic and/or star:
“There is no magic decoding ring that will help us read our young adolescent’s feelings. Rather, what we need to do is hold out our antennae in the hope that we’ll pick up the right signals.”
—The Lions Clubs International and the Quest Nation. The Surprising Years, III, ch.4 (1985)
“...indeed, star differs from star in glory.”
—Bible: New Testament, 1 Corinthians 15:41.