I think that even if we ignore the practicality of building it, at that thickness the neutron star material would immediately collapse into a black hole :)
How about a whole system of neutron stars, in orbit around each other, separated by vacuum, arranged for a given straight-line path in order that at any point in time that path intersects at least 189 km worth of neutron stars?
Is this possible? I'm considering a loose definition of the word "possible" here, but could such an arrangement exist without collapsing to a black hole under gravity or being torn apart by centrifugal force?
>How about a whole system of neutron stars, in orbit around each other
that's a neat idea. the orbital mechanics involved are pretty mind-boggling, but I guess a civilization that could create a system of neutron stars could probably deal with the math ;).