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Clearly, it is possible to build the prop if you have the budget of a TV or movie production. You can order acrylic cylinders from the factory, though they are probably too sturdy/heavy. Or, you can form a thin acrylic sheet into a half-cylinder using a heat gun. But either way, it's probably not going to be cheap.
Then I thought "What if you could buy something already made that would serve the same purpose?"
To cut to the chase, what you want to look for is a used retail floor display cabinet. A rectangular glass box is pretty common, just take the glass shelves out of it, and it might even have lighting installed in it already. If you're really lucky, you might even find one that is round, or at least six or eight-sided.
If you're in a major city, there are probably companies that resell used retail fixtures, and in the current business climate, they probably have a lot of stock on hand.
Other possibilities might include something like this curio cabinet, if it could be made to work:
http://www.wayfair.com/Floor-Standing-5 ... A1043.html
You might even be able to find an old phone booth that would work.
Safety note: whatever you do, you should mount the cabinet onto a large heavy base, so that there is no chance of it tipping over. I'm thinking a 48" square of heavy duty plywood, with carpet glued over it.
