How many edges does cyclinder have?

It is a 2-dimensional sheet that is rolled together and has 2 ends, so it has 2 edges.

However, if the cylinder was a 'planck length' thick [10 to power of -33 cm; in other Words extremely thin - as thin as you could get ] it would have no edges since it has no 'locality' ! (And that is a scientific fact - I am not making it up.)

So, if it was 1 planck length thick, how many dimensions would it have - one or two? Think that one through!