The Garden of Professor Möbius - Solution

Red solid arrows are on the top visible face of the pathways. Green chain line arrows are on the rear invisible face.

Truth to tell I don't know if this the shortest route possible. Aside from mirror image variations, it is the only route I have found. However I have no proof that it is a unique solution.

Do please let me know if you think you have done better or, indeed, found any alternative solution.