Be sure to pack a lunch and take lots of pictures.
Now, if you square that cube, what you get is a three-dimensional representation of a four-dimensional object - a tesseract. It has eight (I think) cubes, all sharing sides and is probably impossible to picture. If it were really four-dimensional, it would look - to us - like a cube, the fourth dimensional aspect being that all eight cubes occupy the same space. Only not exactly. But it would really mess with space and time, as the short story admirably demonstrated (one man chases himself around a four-dimensional house, which folds itself entirely into four dimensions and vanishes somewhere with a pop, leaving the characters stranded miles from their starting place. He explains things much better, find the story if you're interested.)
Anyway, I'm back.... so, what did you do today?