The ant

An ant travels on a parallelepipedic box.
Say with size 1m × 2m × 4m.
What is the shortest path from A to B.
Say from point A at h = 10cm of midpoint of the shortest edge
and B at opposite side.

And now h = 20cm ?  Solution
An what if h = 30cm ?  Solution

And even more, for the pros :
A room 1m wide × 1.20m height × 1.24 length



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