A glass-shader produces a render like this:
Adding a transparent shader creates
Where does the border labeled as 1 come from? Why is the outer region (2) more translucent than transparent? Not sure this is a material or lighting issue.
With out a subsurf modifier it looks terrible:
I tried several values from the IOR range 'Glass': 1.440 - 1.900
Only the upper edges and bottom are beveled.