which would make the 4-D component 0.
To be honest I'm not really sure how 4-D rotations work. I know about the simple rotations but not the mechanism in how it rotates, and I'm not sure whether to use a simple or a double rotation in this case. Other than that I can do rotations in less than 4 dimensions.
If someone is aware of an additional piece of information, that would help solve my whole problem, would be the the transformation of a unit vector along one of the axes into the long diagonal of a unit hypercube. The scaling is easy (multiply by $\sqrt{d}$) for any dimension $d$ but I can't get the rotation down.
Thanks in advance.