I found the same site bshelle posted, "The materials used and the various processes involved in creating Dreamspheres are a closely guarded secret.
The spheres are not made from glass as might be expected, but are many times stronger than glass.
They are made from a combination of materials that are unique to the Dreamsphere."
I say lucite, they're only like 50.00, I looked it up and he had a sale for 30.00, not sure he would do that with glass, it just looks like plastic too. I think glass would be even more dynamic.
I've seen cellophane fantasy film in these exact colors. Grab some sample sheets and throw them into a plastic globe
If you want it to look closer to that I would adhere the film to plastic sheet, slice them up and add it that way.