Trisection of a cube with internal storage

I wondered if I could hollow out the trisected cube and actually come out with a useable storage compartment. Turns out, it works. If you're storing just one big thing, it needs to fit into the void of just two pieces (i.e. in 2/3rds of the sphere). Multiple items inside can use more than that, as they can slide out of the way for the leading edge of the final trisection to pass through when you close/open the piece.

I printed it scaled up to take up most of my print bed, as seen in the ph