In reality however, it is quite simple.
We have only to remember that the tesseract is generated by the movement of a cube, in a direction at right angles to every direction that can be drawn in the cube, and that whenever a figure of a given dimensionality moves thus it generates a figure of the next higher dimensionality.
Thus every point in the cube will trace out a line, every line a surface, and every surface a solid, and, since the distance moved is equal to the length of the side of the cube, these surfaces will be squares and the solids will be cubes.
But let us first consider the analogous case of the generation of the cube by the movement of a square.
Let A B C D represent the original position of the square. It moves, a distance equal to one of its sides, in a direction at right angles to every direction that can be drawn within itself—at right angles, i.e., to every one of its sides—and finally comes to rest in the position E F G H.
Fig. 12
Every side has traced out another square and we have, in addition, the old square ABCD, with which we started and the new square EFGH, with which we end.
Thus even if we had no idea how many sides, edges, and corners a cube had we could deduce them.