You need to use what is called a light tent. These can be bought from professional photographic suppliers. Try looking in the small ads in Amateur Photographer. It may not be cost effective if this is just a one off.
Alternatively, surround the crystals with opalescent sheets (from art supplies shops), or even some old sheets and fire one or more flashguns through. To hide the camera and also to help with adding light to the subjects, get a large piece of polystyrene (from DIY stores, but quite large), cut a hole just big enough to poke the lens through. This may sound very complex, but there are professional photographers out there who specialise in this kind of photogaphy.