The following is taken from the site "What is Four-Dimensional Space Like?"
If you were to live in a tesseract, you might choose to live in its three dimensional surface, much as a two dimensional person might choose live in the 6 square rooms that form the two dimensional surface of a cube. So your house would be the eight cubes that form the surface of the tesseract. Imagine that there are doors where ever two of these cubes meet. If you are in one of these rooms, how many doors would you see? What would the next room look like if you passed through one of the doors? How many doors must you pass through to get to the farthest room? How many paths lead to that farthest room? Could you have any windows to outside the tesseract? What about windows to inside the tesseract?
Some of these questions are not easy. To answer them, go back to the easy case of a three dimensional cube with faces consisting of squares. Ask the analogous questions there and just extrapolate the answers to the tesseract.
