You probably already saw such a representation of the tesseract:

I did something similar on my blog for the truncated tesseract:

The vertices in 3D are the stereographic projections of the original 4D vertices. This point is clear. However I don't know how the varying radius of the bent tubular edges should be chosen. To get a bent 3D edge, I project the corresponding 4D edge on the 3-sphere and then I stereographically project the bent 4D edge. But how to choose the radii? The way I use on my blog consists in arbitrarily taking a radius "proportional" to the norm of the 3D point (e.g. I take $\log\bigl((1 + \Vert M \Vert)/4\bigr)/4$, because I empirically found this choice yields a pretty result). Is there a mathematical consideration that would justify to have a radius "proportional" to the norm of 3D point? What is the meaning of the value of the radius?