It's a Verner Panton-style moon lamp. FOUND IT! My bet is that my find is the one they actually use on-set. Found one in the UK- -the owner says the manufacturer is Invicta but I can't find a match with that name. In the US LumiSource has a nice inexpensive version.
This flexible, yet strong, phone charger could come in handy (especially in a car to display a map)