Ant and honey on the prism and cylinder – part 3

An interesting mathematical game: “What is the shortest path between an ant and a drop of honey?”, got its sequel…

ABSTRACT

The third version of “Ant and Honey on a Prism and a Cylinder” shows that a triangular prism and a hexagonal prism have not two, but even three shorter paths (shorter than the obvious path).
As before, the square prism has two shorter paths, and the cylinder has one.
It is interesting that a triangular prism, a square prism and a hexagonal prism are the only prisms that can completely fill (three-dimensional) space.