  In extended Heisenberg-Kitaev-Gamma-type spin models, hidden-SU(2)-symmetric
points are isolated points in parameter space that can be mapped to pure
Heisenberg models via nontrivial duality transformations. Such points
generically feature quantum degeneracy between conventional single-q and exotic
multi-q states. We argue that recent single-crystal inelastic neutron
scattering data place the honeycomb magnet Na$_2$Co$_2$TeO$_6$ in proximity to
such a hidden-SU(2)-symmetric point. The low-temperature order is identified as
a triple-q state arising from the N\'eel antiferromagnet with staggered
magnetization in the out-of-plane direction via a 4-sublattice duality
transformation. This state naturally explains various distinctive features of
the magnetic excitation spectrum, including its surprisingly high symmetry and
the dispersive low-energy and flat high-energy bands. Our result demonstrates
the importance of bond-dependent exchange interactions in cobaltates, and
illustrates the intriguing magnetic behavior resulting from them.
