  Dual topological insulators (DTIs) are simultaneously protected by
time-reversal and crystal symmetries, representing advantageous alternatives to
conventional topological insulators. By combining ab initio calculations and
the $\mathbf{k}\cdot\mathbf{p}$ approach, here we investigate the electronic
band structure of a Na$_2$CdSn tri-atomic layer and derive a low-energy
$4\times 4$ effective model consistent with all the symmetries of this material
class. We obtain the effective Hamiltonian using the L\"owdin perturbation
theory, the folding down technique, and the theory of invariants, and determine
its parameters by fitting our analytical dispersion relations to those of ab
initio calculations. We then calculate the bulk topological invariants of the
system and show that the Na$_2$CdSn tri-atomic layer is a giant-gap (hundreds
of meV) quasi-2D DTI characterized by both spin and mirror Chern numbers $-2$.
In agreement with the bulk-boundary correspondence theorem, we find that a
finite-width strip of Na$_2$CdSn possesses two pairs of counter-propagating
helical edge states per interface. We obtain analytical expressions for the
edge states energy dispersions and wave functions, which are shown to agree
with our numerical calculations. Our work opens a new avenue for further
studies of Na$_2$CdSn as a potential DTI candidate with room-temperature
applications in areas of technological interest, such as nanoelectronics and
spintronics.
