torc ring moebius pentagon

My father wished for that model and I gladly obeyed :-)
He wished for a closed ring where the profile of a pentagon rotates one time in itself while on its way around. That means the pentagon has the same position 5 times. As I was building it I decided to make an second version where it would rotate one time less and connects to the next surface instead of the same when it arrives at the beginning. That would create an infinite long surface. It would only have one long surface instead of five.