Consider cardinal directions in a variety of circumstances. Although four directions at 90° angles does work nicely on a plane or locally on a sphere - or even globally with some distortion - other systems also work on these topologies and even on some others, and some topologies won't play nice with four 90° angles in a plane.
Now the polynesians if I have understood correctly did not rely exceedingly much on stellar navigation. However, a similarly sea-faring people could easily require a set of directions involving height so as to be able to quickly communicate and maintain skills related to stellar navigation.
To make this interesting, let's have 120° degree angles between the basic directions, and the points in the air are at a 60° offset, so combinations of a plane-based direction and a height direction exist in an inclined plane.
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