Topology routinely considers spaces of dimension higher than
three and some of those are much stranger than the "nice
rectangular" spaces you might ordinarily think of. You might
look at a few topology books and see if you can find one that
meets your needs, but topology covers lots of other things and
you might have difficulty finding just what you want. Steenrod,
if I haven't gotten him confused with another name, wrote a book
in the last twenty years that specifically described one method
of visualizing 4 space. Unfortunately my copy is buried so deep
that I'll likely never find it again. Charles Howard Hinton was
an individual about a century or a bit more ago who wrote
several books on the fourth dimension. Dover I think published a
chopped up version of parts of this about 40 years ago, but some
university libraries might have reprints of Hinton's originals.
He had what was claimed to be an astonishing memory. In his book
he described a set of colored cubes where the colors showed how
the faces would be