When thinking on a fourth spatial dimension, it can be useful to grasp the 3D shadow of such 4D objects in our spatially 3D world. Now, human vision is inherently 2D dimensional (it involves two projections in our retinas plus complex brain processing to reconstruct a 3D understanding of the world from those 2D projections).
Touch, on the other hand, it is inherently 3D, helped by our sense of propioception, which give us 3D awareness of our body parts. The idea is thus to make a device that allows people to touch the shadow of 4D objects. How to make such device? It might possible to 3D print different models but that'd be slow. Simpler 3D projection devices can communicate elevation by means of variable height pins. An intriguing alternative would be to use a ballon with strands of electrically activated material.