The rope must not be less than 10 centimetres (100 mm), or more than 12.5 centimetres (125 mm) in circumference...
Since it's declaring a negation, shouldn't it be nor?
Nor is generally only used in conjunction with neither, so you could rewrite the sentence as:
... but that's not necessary. The sentence is just fine as it stands.
You're parsing the sentence as if "not" and "or" were in opposition. They're not: "less" and "more" are the alternatives here. It might make more sense if you strip it down to:
Although there are some people who are afraid to use nor without neither, that seems silly to me. I would certainly have written nor there in your example sentence. The OED supports this very sort of thing in its sense 3a for nor conj.1 (and adv.), which is:
Here are two of its citations for that sense:
See? Perfectly natural. Your sentence involves an instance following not, which is directly covered above. I would have used nor.
There are other senses of nor without a corresponding neither, but I shall not list those here.
Nor shall I list them down here.
Nor here, either. :)