The fact, by the way, that there is a figure equivalent to the cube–i.e. a
sort of super-cube–in any number of dimensions, provides the answer to the
question in my subject line. A 1-inch square (i.e. every one of its sides
is just 1 inch long) has a longest diagonal whose length is the square root
of 2. A 1-inch cube (every edge 1 inch long) has a longest diagonal whose
length is the square root of 3. A 1-inch 4-dimensional hypercube has a
longest diagonal whose length is the square root of 4. And so on. This is
a general rule: A 1-inch n-dimensional super-duper-hypercube has a longest
diagonal whose length is the square root of n. The Empire State Building is
around 15,000 inches high, and that is the square root of 225,000,000. So
if you construct a 1-inch cube-equivalent in a space of 225 million
dimensions, the ESB will fit into it very nicely.