There are existing projects for this, for example [1]. I haven't tried OP demo yet (but I've spent a fair amount of time thinking about 4D and VR and implement

There are existing projects for this, for example [1]. I haven't tried OP demo yet (but I've spent a fair amount of time thinking about 4D and VR and implemented my own viewers), and I'm very convinced that the cross section approach is much much better if you want to deeply understand what is happening. The perspective projection folds the fourth dimension into our hyperplane and you can't untangle it. To paste something I wrote here [2], regarding the difficulty of groking the tesseract from the projected figure, I think it’s almost impossible to realize that there are points inside the tesseract that are not inside any of the eight cubes visible in the [projected] image, or that if you trace a diagonal between the corners of the tesseract you do not pass through any of the eight cubes. There is much more space inside the hypercube than meets the eye in the perspective projection. [1]: https://www.youtube.com/watch?v=BFmDLUUhZjE https://www.youtube.com/watch?v=BFmDLUUhZjE [2]: http://1å.fr/blog/down-the-4d-rabbit-hole-navigation/ http://xn--1-2fa.fr/blog/down-the-4d-rabbit-hole-navigation/