Flexing Characteristics

In connection with the flexing operation, the relationships between the right and left flexing flexagons should be discussed (The right or left flexing aspect of a flexagon will be called its flexing characteristic.). We have seen that the difference between right and left flexing flexagons lies in the way the flexagons are wound up. What changes, then, can be made in the plan of a flexagon with one characteristic to convert it into a flexagon of the other characteristic. That is, how can a plan be made to wind up the other way? Perhaps the most obvious is interchanging the number sequence numbers on the back and front of a plan. Thus, if

+	+	+		+	+
1	3	3	...	1	1
2	2	4	...	N	2

represents a left flexing flexagon, then

+	+	+		+	+
2	2	4	...	N	2
1	3	3	...	1	1

represents a right flexing flexagon, all else being equal. Another way of changing the flexing characteristic is by changing all signs in the sign sequence. If the tetraflexagon

+	+	+	-	-	-	+
1	3	3	1	5	5	1
2	2	4	6	6	4	2

is a left flexing flexing flexagon, then the flexagon

-	-	-	+	+	+	-
1	3	3	1	5	5	1
2	2	4	6	6	4	2

is a right flexing flexagon. Now, if we look at these plans, it becomes apparent that they are no more than mirror images of each other. In fact, if we watch the flexing operation of a left flexing flexagon in a mirror, we see the operation of a right flexing flexagon. A right flexing flexagon is the mirror image of a left flexing flexagon.