What is a sweater with a close-fitting collar that folds over and covers the neck called?

What was described is a turtle that, not a polo. A "polo" collar has a folded down collar, similar to what a golf shirt is.

Leslie Oakley, I agree. I never heard a turtleneck called a polo neck.

it's called turtle neck

It’s called a turtle neck

Turtle neck

Can't Touch This, I never liked those style of tops because I don't think that they are very flattering around the chin area if you wear the snug fitting polo neck