If I may get back to the original topic. I don't think the 1:4:9 ratio has any great significance - it's a nice integer sequence but there are plenty of other nice integer sequences.
What I feel does have significance isn't even remarked on in the book - that the sides are at right angles. It seems trivial, obvious even, but I see importance in extending to higher dimensions.
You may be familiar with the Platonic solids, and how there are five and only five. In four dimensions there are six regular "polytopes", but beyond that there are just three series that work for any number of dimensions. One are the hypercubes, and they can be seen in a way as the units of space - at each vertex the edges all meet at right angles. The hypercubes can tessellate space, and for example could be combined to make a 1:4:9:16:25:... ratio Monolith (at least conceptually); I think the hypercubes might be the only family of regular polytopes that can fill space.
To get into more familiar terms, suppose instead that the "Monolith" had been an icosahedron. In three dimensions that would be no less perfect than the cuboid, in fact arguably more perfect. But it doesn't extend into higher dimensions. There's no 4D polytope made of icosahedra. A dodecahedron would extend to 4 dimensions, making a polytope called the 120-cell, but no further.
So really, the Monolith had to be a cuboid.