If you take a closer look of these two magic circles, you will find out that the circles within each magic circle are just the inside out reversal of those in the other magic circle.  The innermost circle of one is the outermost circle of the other.  The outermost becomes the innermost, and by the same token for the second and the third circles.  It is clear now, it is a matter of permutation.  A permutation of the four circles is the secrete.  You can produce a total number of 4! = 4 x 3 x 2 x1 = 24 magic circles for this particular magic figure.  That means 22 more magic circles can be created.

By the same reasoning, a total of 24 magic circles can also be created for Fai Young's magic circle series.  Beside Fai Young's magic circle, 23 more magic circles can be produced by a simple permutation of the four circles.

22 more for the first series plus 23 more for the second series becomes 45 new magic circles.

Of course, each magic circle can create a magic polyhedron.

SOME MORE... (The following was written on November 26, 1999.)

From the above discoveries, you can found a total of 48 magic circles. However, the mirror image of each one of them is also a magic circle. That means you can also create another 48 magic circles in addition to the original 48 magic circles. Now, a total of 96 magic circles are formed, and each magic circle, of course, can create a magic polyhedron.

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