Cyb- I am a Bryce user ... Obsolete but capable. But keep in mind that this is an impossible shape that breaks all the rules of 3D space. Probably the best I could do is set some surfaces up in Bryce at the correct angles, reflect stuff off of them and then clone some of those effects onto the impossible shape's surfaces. But first I'm going to get the background in place, see how everything balances out.
Also, as much as I love tasty reflective effects, I really don't see much of that kind of thing in hyperspace- colors tend to be very smooth and saturated, and don't seem to react to external light sources but instead provide their own lighting and color. That's the look I'm trying to aim for here.