Nuclei contain almost all the mass of normal baryonic matter. What if matter is compressed more and more? Where can we find such kind of matter? Why should one be interested in it? What could be its state? These are essentially questions of the fundamental strong interaction between quarks at low-energy scale and hence of the non-perturbative quantum chromo-dynamics, the solution of which would certainly be meaningful for us to understand one of the seven millennium prize problems (i.e., "Yang-Mills Theory") named by the Clay Mathematical Institute. Our answer to them is: compressed baryonic matter can be created during supernovae and it is composed by quark-clusters the interaction between which might be Lennard-Jones-like.