  Quasiparticle excitations of free electrons in condensed-matter physics,
characterized by the dimensionality of the band crossing, can find their
elementary-particle analogs in high-energy physics, such as Majorana, Weyl, and
Dirac fermions. While crystalline symmetry allows more quasiparticle
excitations and exotic fermions to emerge. Using symmetry analysis and {\it
ab-initio} calculations, we propose that the 3D honeycomb crystal
NaCu$_3$Te$_2$ hosts triply degenerate nodal points (TDNPs) which are perfectly
separated from the bulk states. We find a tunable phase transition between
TDNPs and a weak TI triggered by a symmetry-allowed perturbation, and we
further reveal the crucial role played by the spin-orbital coupling (SOC) for
the emergence of the TDNPs in this system. Such topological non-trivial ternary
compound not only serves as a perfect candidate for studying three-component
fermions, but also provides a beautiful playground for understanding the
topological phase transitions between TDNPs, TIs and trivial insulators, which
distinguishes this system from other TDNP candidates.
