Also I think we may have the binary inversed.
It could be {4, 6, 3, 5} as opposed to {3, 1, 4, 2} as we have all assumed. Note there are 5 sections between the graph lines on each side of the equator in the diagram. Hence there would be five sections around the perimeter per 1/4 turn. (Note: I am not sure if this is valid or if it ties into the 3D coordinates hypothesis I posted before but it's just a thought.)
So here is my really crappy phone sketch as to why:
It could be {4, 6, 3, 5} as opposed to {3, 1, 4, 2} as we have all assumed. Note there are 5 sections between the graph lines on each side of the equator in the diagram. Hence there would be five sections around the perimeter per 1/4 turn. (Note: I am not sure if this is valid or if it ties into the 3D coordinates hypothesis I posted before but it's just a thought.)
So here is my really crappy phone sketch as to why:

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