  We show how the two-dimensional (2D) topological insulator evolves, by
stacking, into a strong or weak topological insulator with different
topological indices, proposing a new conjecture that goes beyond an intuitive
picture of the crossover from quantum spin Hall to the weak topological
insulator. Studying the conductance under different boundary conditions, we
demonstrate the existence of two conduction regimes in which conduction happens
through either surface- or edge-conduction channels. We show that the two
conduction regimes are complementary and exclusive. Conductance maps in the
presence and absence of disorder are introduced, together with 2D
$\mathbb{Z}_2$-index maps, describing the dimensional crossover of the
conductance from the 2D to the 3D limit. Stacking layers is an effective way to
invert the gap, an alternative to controlling the strength of spin-orbit
coupling. The emerging quantum spin Hall insulator phase is not restricted to
the case of odd numbers of layers.
