Since then, I have been acting as his eyes into 4-dimensional space, seeing fascinating and beautiful objects such as the 24-cell, the 48-cell and the runcinated tesseract, on his behalf. I have shown him what a 3-sphere looks like, as well as other interesting round things in my world such as cubical cylinders, spherical cylinders, and duocylinders. He has seen a good number of conical objects: cylindrical cones and spherical cones (which, incidentally, is what a light-cone in your world looks like); but he has hardly begun to see all the other cool things in my world, such as knotted spheres and Klein bottles (which, by the way, don't hold any water in my world, in spite of the name), not to mention such oddities as the real projective plane, which can be embedded in my world without intersecting itself.
Recently, I have begun to teach him the basics of manipulating objects in my world, using a 4D Building Blocks game and a 4D Rubik's Cube.
If you're curious to know more about the 4-dimensional space where I live, I'd suggest you begin with the polychora, especially with shapes other than the tesseract (for example, consider the beautiful 24-cell which has no direct analogue in your world). I am rather tired of being the center of attention all the time; besides, more insight can be gained by exploring other 4-dimensional objects than being limited merely to looking at boring ol' me.
