I don't recognize the bed frame -- it's indeed beautiful - but I can tell you that our mattresses are a great match with sleek contemporary bed frames like this one. Somnium mattresses are just under 8" in height and they are a great option for modern bedrooms that require a low profile. We make them in all American, European and custom sizes, too.
In bed frames like these, the mattress and support (either a platform or a slatted frame) are usually slightly recessed into the frame, as seems to be the case here. I'd say the part you see is probably only the top 5".

where is the square hanging fixture over the bed from?