Q about magnetic buckyballs and knots

DeadWolfe

This about those magnetic toys buckyballs. My apologies, I don't really know any physics, so sorry if my terminology is confusing.

If one lines up two lines of buckyballs they can be lined up with the same orientation, (ie as they are in the cube when you get them) or oppositely (so that each ball in the top row touches two in the bottom row).

One can make this into a Mobius band iff the they are lined up in the opposite orientation. Likewise, it can be made into a knot iff they are oppositely oriented, or one inserts a twist.

If we make a rectangle of buckyballs 3 lines thick, we get the same result iff all three rows are oriented the same, or if they all alerternate orientation, but not if there are two the same next to each other and one different.

In general, for a rectangle of buckyballs n-layers thick, which orientations can one make a mobius band out of? Which knots can one tie?

ImaLooser

If one lines up two lines of buckyballs they can be lined up with the same orientation, (ie as they are in the cube when you get them) or oppositely (so that each ball in the top row touches two in the bottom row).

That is kind of confusing. You are saying the alternative is to have each ball in the top row touch one in the bottom row? It is hard to think of of a good word for this, so I see the problem.