The Cosmic Hexahedron is where Octahedron resides. It's a cube that has a door on it. The door doesn't have a handle, so one can only presume Octahedron is the only one who can access the inside (except for when he isn't, because there are definitely beings higher than him and can easily barge in at any time. once they enter, though, they're kinda screwed). The inside of it is basically S P A C E except you can breath. Also, there's that royalty free elevator music constantly playing.