There's no difference between phone and fax numbers. To make a regular expression, you'd have to ask yourself a couple of questions:
Do you require an area code, or will 7 digits be acceptable? Do you want to validate the area code as well?
In the US, it's not uncommon to use letters instead of digits. Is your regexp going to allow that?
Do you insist on separators? Are the optional? Forbidden? If they are separators, can they be dashes? Spaces? Either, but not mixed? Allowed elsewhere than the standard 3-3-4 grouping? Can you have parenthesis around the area code?
Do you require a leading 1? Is it optional? Do you allow the international '+' prefix?
What about extensions? Allowed? If so, for how many numbers?
It's possible to hook in a fax into a 911 dispatch center, making it a 'fax number' as well. Are you going to allow that as well?
Depending on the answers, your regexp can be as simple as /1[0-9]{10}/, or something far more complex.