I have studied some things about four dimensional geometry from the internet. I understand what the fourth dimension is and I can draw a hypercube an so on. The problem is that I can't imagine four dimensonal things. Can someone? How can I learn for example to turn a hypercube around in my mind?

If you think you can fully imagine four dimensional things, think again. Can you for example tell how many octahedrons does it take to make a polychron (which means a four dimensional "polyhedron"). You can easily imagine how 4 triangles make a tetrahedron and 8 triangles make an octahedron. What about any fourdimensional object?