Here is a representation of five subspaces – the image on the left is one subspace, the second one has a second subspace layered onto it and so on. The fifth image is the CQC. Why is the Compound Quasicrystal important? It is important because of its relationship to the QSN. The QSN (Quasicrystalline Spin Network) is the densest possible (under certain constraints) 3D network of point-sharing Fibonacci chains and is the most computationally efficient point space in 3D. When we talk about the densest 3D Fibonacci chain, we are talking about two letter chains instead of the infinitely inflated chains, which is a property of QSN as a quasicrystal. The QSN is created by taking the FCC lattice (a point space that provides the densest packing of 3D spheres) and then spreading its points until they are spaced according to the Fibonacci sequence. We populate this new, extended point space with tetrahedra that point up and that point down.