The recent discussions about neutron stars provoked the following question. This question isn't about neutron stars, per se, but about "nuclear" materials made from the basic stuff of neutrons & protons. We've been assuming that materials such as this can only exist inside neutron stars which are held together by extremely high gravity, but I'm not 100% convinced. For example, we used to think that diamonds could only be made under extreme pressure, but this has been found to be false; diamond coatings can be made with with chemical vapor deposition (CVD) under relatively low pressure. http://en.wikipedia.org/wiki/Synthetic_diamond. What I'm thinking of is a kind of "foam" which is a more-or-less fractal material made out of nuclear "soup" (protons-cum-neutrons). Think Sierpinski pyramids or Apollonian foams. Since the material is mostly empty space, it could be considerably less dense than the stuff of neutron stars. What I'm hoping for is some sort of quantum effect that enables this "foam" to keep from collapsing, and hence have some rigidity, but perhaps also have some decent strength, so that it could exist in macroscopic form. (There is also the problem of "nuclear" stability, but perhaps there are wave functions which are stable due to the geometric form of the structure.) Now the biggest problem is why we haven't seen this stuff already. The fact that we haven't seen it before merely indicates that it may take very special conditions to form it -- e.g., a _manufactured material_ or some sort of collision of two neutron stars. I don't know enough physics to guess whether such a material could really exist, which is why I'm posing the question.