Okay so I see how I end up with a Vector3(y/x, z/x, w/x) if x is larger than y/z/w for example. Let's say the vector is (-1, -1, 1). I understand how this always lies within a unit cube around the origin.

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!

But then you say there are four variables, that means we get four of these cubes. This sounds, to me, like I need to then do the same procedure but not with Vector3(y/x, z/x, w/x) but Vector3(x/y, z/y, w/y) for example? Is this correct or am I misunderstanding you? If this is the correct procedure, then the largest absolute value part is confusing me, do I just let that determine the quaternion element that I start with?

Lots of questions here, sorry! I hope you have (or someone else has) some time to explain the concept some more!

In order to save memory we want to rotate the billboards via code ourselves! The 17 pitches also do not describe a full 360 deg turn, since we only need half a circle. Then the other half of pitches can be translated to a different set of pitches with a 180 deg yaw rotation, if that makes sense! So: 32 yaw angles = 360 deg yaw rotation, 17 pitch angles = 180 deg pitch rotation, no roll angles = rotating via code!

Hmmm... Nothing for roll?The 544 angles are 32 yaws and 17 pitches!