It's the......
...Fender Precision Scoopback. The back is carved out to accomodate beards.
(The Fretful Porpentine, Mon 29 Sep 2003, 17:30, archived)

they think of everything
those plucky americans
(psausage76, Mon 29 Sep 2003, 17:32, archived)

Actually...
....I think Leo Fender who designed the precision bass was Polish. They are notorious beard wearers so one could assume it was part of his original design.
(The Fretful Porpentine, Mon 29 Sep 2003, 17:33, archived)