  We investigate the ground-state nature of the honeycomb Kitaev-$\Gamma$ model
in the material-relevant parameter regime through a combination of classical
and quantum simulations. The classical model is imprinted with a tangle of
highly structured spin double helices. This helix tangle exhibits $18$
inequivalent helical axes and features a spontaneous periodicity anisotropy and
a ${\rm sgn}(\Gamma)$-determined chirality pattern. Infinite PEPS simulations
with clusters up to $36$ sites identify hallmarks of this many-body order in
the quantum spin-$1/2$ model. Our findings provide a fresh perspective of the
Kitaev-$\Gamma$ model and enrich the physics of Kitaev magnetism.
