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If we consider a square made of arcs of equators on a sphere. The interior angle on the sphere is chosen to be 108°.

Then the sphere is rolled along those arcs on a plane.

The square hence draws segments with a 108° angle between them. On the plane this closes only if we roll the sphere twice on one segment and it draws a pentagon.

Hence the sphere had to be rotate 5/4 times 360°.

Could this in some sense describe a spin 4/5 system ?