A high coordination lattice has an underlying cubic lattice with unit length less than 3.8/N Å for some integer N > 1. Cubic lattice points are connected in the high coordination lattice if their Euclidean distance is between 3.8 ± ε for some ε > 0. The high coordination lattices used here are named HC4 and HC8 corresponding to their N value (4 and 8). The ε value is 0.2 for all HC lattices. Figure 3 shows an illustration of a 2D high coordination lattice with N = 3 and ε = 0.4. High coordination lattices have previously been used for protein structure prediction[23,24]. Note that the SCC and FCC lattices both have the excluded volume property, meaning that atoms at two different lattice points will never collide. This property does not necessarily hold for high coordination lattices, and collisions must therefore be detected explicitly.