I mean actually VISUALIZING. Like, when you close your eyes you can still visualize a three-dimensional world, because you know it's out there.
I find the '2D-3D projections of a rotating hypercube' don't do it for me. I mean, I KNOW what it's supposed to be, why the small cube turns inside out into the big cube and then back, etc. etc., but I can't actually visualize it in four dimensions. (This guy made a 'tesseract trainer'. Very beautiful indeed, and I intend to keep trying, but it hasn't done anything for me yet.
Link )
If you can actually 'see' into extra dimensions with your mind, how did you acquire this skill?