Referring to the link supplied by SpruceMoose, cutting and gluing plexiglas is one way of doing it.
Though I should note that Plexiglas can be bend easy (more or less) enough. I've only worked with smaller pieces, but I clamped it in between two pieces of wood at the point were I wanted it to bend. Then heated it with a heat gun (heat gun, like a hair dryer only much hotter). When it was hot and soft, I used another board to press it from behind and bent it over the first board.
You could cut the plexiglas or acrylic-glas into something of a 'plus' shape or a 'cross' shape, then bend that tabs over into a 5-sided box. Now you just need a way to close up the corners. Several possibilities come to mind, but really it just requires some ingenuity and imagination.
As an alternative, assuming you like the look, you can buy right angle or L-shaped wood molding in various materials (oak, pine, etc...). You could build a frame from this L-Shaped molding and glue flat pieces of plexiglas or acrylic-glas to the inside of the molding.
Between the molding, the glass, and the glue, it should hold together nicely.
The hinge is the hard part though. There are assorted woodworking shops that might have a hinge you could use, but I think it will be difficult to come by. Especially a hinge that allows the dust cover to be removed.
I think, for a hinge, the best you could hope for is a trashed out turntable that you could salvage the hinges from.
Though may turntables have dust covers that don't have hinges. In this case, just leave enough room behind the turntable to prop the dust cover against the wall until you are ready to put it back on again.
Just a few thoughts.
Steve/bluewizard