  We generalize the concept of triply-degenerate nodal points to non-collinear
antiferromagnets. Here, we introduce this concept to insulating quantum
antiferromagnets on the decorated honeycomb lattice, with spin-$1$ bosonic
quasiparticle excitations known as magnons. We demonstrate the existence of
magnonic surface states with constant energy contours that form pairs of
magnonic arcs connecting the surface projection of the magnonic triple nodal
points. The quasiparticle excitations near the triple nodal points represent
three-component bosons beyond that of magnonic Dirac, Weyl, and nodal-line
cases. They can be regarded as a direct reflection of the intrinsic spin
carried by magnons. Furthermore, we show that the magnonic triple nodal points
can split into magnonic Weyl points, as the system transits from a
non-collinear spin structure to a noncoplanar one with a nonzero scalar spin
chirality. Our results not only apply to insulating antiferromagnets, but also
provide a platform to seek for triple nodal points in metallic
antiferromagnets.
