Keith:
It is a fazzoletto, or at the very least, fazzoletto style, as all that does is describe a particular look. I'm pretty sure it's not a very good maker as the zanfirico is fairly loose and irregular, and the plain stripes are very simple. The pontil mark looks rough but they're rough on many of even a good makers like Salviati.
The id problem is that, although Venini is associated wit the style, which was actually an adaption of a design by somebody else, every glass maker under the sun seems to have made a version of it, from Italy to Britain, China, and to Canada, even.
David
PS I wrote this while Tambam was posting. I think we agree. The difference is that I think it's fair to call a piece a fazzoletto, if it looks like a Venini fazzoletto. If Venini can adopt a look, then so can other firms. The difference is that the Venini pieces generally have better workmanship and usually have a certain gracefulness.