Yes, w is included. Imagine x has the largest absolute value. Then you compute (y/x, z/x, w/x), which has each coordinate between -1 and 1. In that sense, it is a cube. Since there are 4 variables, you get 4 different cubes. This is similar to the situation with cubemaps, where you map a point in a sphere to one of 6 square faces.
I'm not exactly an expert with quaternions yet, but I do know the basics (x, y, z define an arbitrary axis around which we rotate by w). How does dividing the other components by the largest one (x, y, z, with w or without?) leave me with a 4 cube division? I don't understand that very fundamental step!
Hmmm... Nothing for roll?
The 544 angles are 32 yaws and 17 pitches!