>>96130823
>If they had, they would have 10
How do you figure that?
There are 8 legs in a cycle. If you represent the legs as corners of an octagon, the edges of the octagon are the positions between legs, of which there are 8.

If you allow non-adjacent pairings then you get
pic related which has 28 edges.
Either 8 if adjacent only (separated by 0 legs)
8 more if separated by 1
8 more if separated by 2
4 more if separated by 3

8, 16, 24, 28 all make sense. How did you arrive at 10?