When time permits, I may try to provide a systematic approach to higher space.
Dimensional analogy is an important tool, when grappling the mysteries of hypercubes and their ilk.
But let's start at the beginning, and to simplify matters, and also bring the focus to bear upon the most interesting ramifications of the subject, let us concern ourselves mostly with regular polytopes. You may wish to explore my links to some rather interesting and wonderful polyhedra and polytopes sites, at the bottom of this page. Yes, we shall be speaking of the fourth dimension, and, well, the 17th dimension, or for that matter, the millionth dimension. In space of zero dimensions, the only figure possible is a point . It has no length, no breadth, no height.