  Hilbert's two-dimensional space-filling curve is appreciated for its good
locality properties for many applications. However, it is not clear what is the
best way to generalize this curve to filling higher-dimensional spaces. We
argue that the properties that make Hilbert's curve unique in two dimensions,
are shared by 10694807 structurally different space-filling curves in three
dimensions. These include several curves that have, in some sense, better
locality properties than any generalized Hilbert curve that has been considered
in the literature before.
