> The easiest way for me to conceptualize it is to think of it as orientation + rotation. 3 dims for the orientation vector to get the object facing/pointing the right way, then a further 1 dim/var for rotation about that axis. For a total of 4 variables/dimensions

Something's missing. Orientation in 3D space is a two-dimensional quantity; you would never need three dimensions to express it. The third dimension has to be providing some additional information, like a magnitude.