I would like to have a precise definition of the topological space called "full-twist" Möbius strip $M$, i.e. a Möbius band with a $360$ degree twist (the usual Möbius strip has just a half-twist).
I don't think that a parametrization in $\Bbb R^3$ would be a good definition. In general, I've seen the usual Möbius strip defined as a quotient of $[0,1]^2$. Could we do the same in order to define $M$ ? I'm not sure how to do it.
Thank you for your comments!