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:
“The echo is, to some extent, an original sound, and therein is the magic and charm of it. It is not merely a repetition of what was worth repeating in the bell, but partly the voice of the wood; the same trivial words and notes sung by a wood-nymph.”
—Henry David Thoreau (1817–1862)
“It is the star to every wand’ring bark,
Whose worth’s unknown, although his height be taken.
Love’s not Time’s fool, though rosy lips and cheeks
Within his bending sickle’s compass come;
Love alters not with his brief hours and weeks,
But bears it out even to the edge of doom.”
—William Shakespeare (1564–1616)