If you present an example of high-dimensional data I'd be happy to help you reason about how to visualise it (although this is perhaps better suited to StackExchange).
edit: if you feel you need 3D, you've already failed to represent the data clearly
I took a visualization course and to paraphrase the prof. you have a 3d object projected onto a 2d (display) plane and reasoning about depth gives additional mental load, not to mention occlusion. You have to interact with the model a lot to get a view you want. The course was based on old papers about UX with a dash of cognitive science, so take it with a grain of salt.