On the structure of icosahedral quasicrystals

For the 3-dimensional icosahedral quasicrystal structures that are obtained by projection from the 6-dimensional hypercubic lattice and its sublattices, the D6 root and scaled weight lattices, explicit general formulae are obtained for the precise distribution of atomic sites. The "invariants of the line" and both ordinary and generalized Fibonacci pseudo-invariants play significant roles.