Now, if you notice, a square is a line, set at 90 degrees to it's self. So it has 4 sides. as if it was stretched out.
The same is with cubes. The square is replicated, turned 90os and connected to the original/neighbor squares. Now, all of these items are in the same space, so imagine a cube, being 90o to it's self. That is what his pic is. That cube is the shadow of a 4 dimensional object. Now, to explain it's shape and why it has 4 45o lines to it, I shall take a look at a cube drawn on a flat peice of paper. You start with two squares with one of it's corners overlapping the other's corner. Then you draw 4 lines connecting the corners of one square, respectively to the other one. You will notice, if the overlapping corners of the two squares is a square, that the lines connecting the two shapes will be at a 45o angle. This is an example of the shadow of a 3d object in a 2d world. Now if you think about this with a 4d object in a 3d world, it would make sense.
also, it is snip, not sneep. lurn2snip