Do head direction cells represent 2D or 3D direction?

Assuming that the substrate for head direction is based on the posture control system the chart on page 222 in this reference should shed some light on the relationship between the vestibular system and head position:
http://cw.tandf.co.uk/neurophysiology/sample-material/Neurophysiology-5E_Chapter-11.pdf

I have copious references to the basal ganglia and related system as part of the posture control system. These are all older brain structures - I expect rich connections to the older brain spatial systems without even looking.

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