  Single-layer PtN$_2$ exhibits an intriguing structure consisting of a
tessellation pattern called the Cairo tessellation of type 2 pentagons, which
belong to one of the existing 15 types of convex pentagons discovered so far
that can monohedrally tile a plane. Single-layer PtN$_2$ has also been
predicted to show semiconducting behavior with direct band gaps. Full
exploration of the structure-property relationship awaits the successful
exfoliation or synthesis of this novel single-layer material, which depends on
the structure of its bulk counterpart with the same stoichiometry to some
extent. Bulk PtN$_2$ with the pyrite structure is commonly regarded as the most
stable structure in the literature. But comparing the energies of single-layer
PtN$_2$ and bulk PtN$_2$ leads to a dilemma that a single-layer material is
more stable than its bulk counterpart. To solve this dilemma, we propose
stacking single-layer PtN$_2$ sheets infinitely to form a new bulk structure of
PtN$_2$. The resulting tetrahedral layered structure is energetically more
stable than the pyrite structure and single-layer PtN$_2$. We also find that
the predicted bulk structure is metallic, in contrast to the semiconducting
pyrite structure. In addition to predicting the 3D structure, we explore the
possibility of rolling single-layer PtN$_2$ sheets into nanotubes. The required
energies are comparable to those needed to form carbon or boron nitride
nanotubes from their single-layer sheets, implying the feasibility of obtaining
PtN$_2$ nanotubes. We finally study the electronic structures of PtN$_2$
nanotubes and find that the band gaps of PtN$_2$ nanotubes are tunable by
changing the number of unit cells $N$ of single-layer PtN$_2$ used to construct
the nanotubes. Our work shows that dimension engineering of PtN$_2$ not only
leads to a more stable 3D structure but also 1D materials with novel
properties.
