Math disagrees with you. You can view a three dimensional object as projection onto a 2D canvas. I suppose I should add the stipulation of 'n>2', but I'm not wrong.
I have all three on my comp. I agree with doimas on the fact that #s 2 and 3 were pretty bad compared to #1, but I did enjoy the twist at the end of #3
I'll explain
It's like drawing a 3D cube on a paper, now you watch a 3D cube in 2D.
That is a 4D cube, and since we live in a 3D world, we can only watch the 4D cube from a 3D perspective.