Period after "fax"

What are the rules for putting a full stop after a fax abbreviation? Sometimes I see:

Tel.: xxx-xxx-xxx
Fax.: xxx-xxx-xxx

Is "fax" here an abbreviation?

Solution 1:

There is no need for a period. Fax is no longer an abbreviation, but a word in its own right.

Solution 2:

I agree with both Alok and Barrie England in part, but suggest that the term fax was never an abbreviation requiring a period (at least in US), but a short form term.

Consider doctor. The abbreviation in US is Dr. (with a period). But there is a short form, somewhat informal, of doc, or more frequently, Doc without a period.

Similarly, the titles of certain religious figures are Brother and Sister. The abbreviations are respectively Br. and Sr. However, the short form for those terms are Bro and Sis (although such short forms would rarely be used in addressing those religious types).

The term telephone also illustrates the point. The accepted abbreviation is tel. or Tel., but there is a short form, phone that never takes a period.

While I have not done any analysis, a brief rumination leads me to the view that abbreviations almost always consist of letters that exist within the word that they represent. Obviously, there is no x in facsimile.

Solution 3:

'Fax' is an abbreviation of 'facsimile'; though the full form is far more uncommon than say 'Telephone'