Ok! Sounds daft - ten sided circle
Curve from centre of alternate apex verticles peaking at the ends of intermediate verticles.
Delete original circles, guides etc.
Separate rectangle, for body of ribbon?
Drag to path of curves above and 'Follow me'.
Difficulty I had was in persuading 'Follow Me' to follow the whole path.
I kept getting 'Path not Valid' errors so I had to extrude along more than one path.
Ok! Now tell me how it should be done. Please . PM if it's a secret.