  Topological phases stabilized by crystalline point group symmetry protection
are a large class of symmetry-protected topological phases subjected to
considerable experimental scrutiny. Here, we show that the canonical
three-dimensional (3D) crystalline topological insulator protected by
time-reversal symmetry $\mathcal{T}$ and four-fold rotation symmetry
$\mathcal{C}_4$ individually or the product symmetry $\mathcal{C}_4
\mathcal{T}$, generically realizes finite-size crystalline topological phases
in thin film geometry (a quasi-(3-1)-dimensional, or q(3-1)D, geometry):
response signatures of the 3D bulk topology co-exist with
topologically-protected, quasi-(3-2)D and quasi-(3-3)D boundary modes within
the energy gap resulting from strong hybridisation of the Dirac cone surface
states of the underlying 3D crystalline topological phase. Importantly, we find
qualitative distinctions between these gapless boundary modes and those of
strictly 2D crystalline topological states with the same symmetry-protection,
and develop a low-energy, analytical theory of the finite-size topological
magnetoelectric response.
