Neutrons Become Cubes Inside Neutron Stars

I do not understand most of that paper, and probably never will, but can someone explain why they propose cubes?

If I take a crate of tennis balls, and compress it, I expect the balls to first (more or less) form a densest sphere packing, and from there, I expect they will start to deform to look like truncated octahedrons (http://en.wikipedia.org/wiki/Bitruncated_cubic_honeycomb)

Those may be cubic, but it aren't cubes.

Also, since there is no unique densest sphere packing, it would not surprise me if variations on this are possible (http://en.wikipedia.org/wiki/Sphere_packing).

Random question for astrophysicists who might see this - what would neutronium actually look like? As I understand it, color and reflection is all due to interactions with an atom's electrons - and neutronium has none.

Makes me think of the rectangles from 2001 Space Odyssey