I think he was wrong. It's pretty hard but not impossible. You don't visualize them directly as 3D objects though, you visualize 3D objects with metadata attach

I think he was wrong. It's pretty hard but not impossible. You don't visualize them directly as 3D objects though, you visualize 3D objects with metadata attached everywhere. While you navigate the space in your mind's eye you have an extra layer of information that flows with you. Consider Alicia Boole Stott. She created cardboard models of the various cross-sections of the 6 regular polytopes. Including the 24-cell which has no equivalent in 3D, the 120-cell and the 600-cell which are super complex figures. I think if you read her story you'll also be convinced that she indeed visualized the figures. [1] I spent quite a lot of time earlier this year on this visualization exercise on the 4 simplest regular polytopes while working on an toy application to manipulate 4D objects and tesseractic honeycomb in VR. You can have a good grasp of where every edge go and the angle between every faces. I could count the number of vertices and edges of a 16-cell or 24-cell just by navigating around the figure in my head. The tesseract and 16-cell are good starting points. 1: http://www.sciencedirect.com/science/article/pii/S0315086007000973 http://www.sciencedirect.com/science/article/pii/S0315086007...