A Math Forum Web Unit
Mutsumi Suzuki's
Transforming Magic Stars
Contents 
Suzanne's Math Lessons 
Magic Squares 
Tessellation Tutorials
Transforming Stars
First let's look at how to apply the transformation (or exchange) rule to yield stars with the number 1 not at the top, but at an inner corner.
Consider this star:
There are three exchange rules:
 A<>L B<>C D<>E H<>I J<>K
 B<>K H<>F A<>C L<>J D<>G
Rotate the star 60° to the right, use rule 1, and rotate 60° back
to the left.
 E<>H A<>D B<>F G<>K I<>L
Rotate the star 60° to the left, use rule 1, and rotate 60° back
to the right.
 Let's apply Exchange Rule 1:
 Now let's rotate Derived Star 1 180°:
Derived Star 2 is not identical to the original but the number 1 is still on top!
 Let's apply Exchange Rule 3 to the Original Star
and rotate Derived Star 3 60° to the right:
In the case of Derived Star 3, the number 1 is at an inner corner.
Here Exchange Rule 3 is the same as (1) rotating 60° to the
left, (2) applying Exchange Rule 1, and (3) rotating
60° back to the right: after the
rotation, the number 1 is at B; with the
transformation the number 1 moves to the inner corner.
On to Combining exchange rules
Back to Magic star sets
