Refined hierarchy of vertices in icosahedral quasicrystals

Imperfect icosahedral quasicrystals are assumed to grow obeying a local rule forcing the twin orientation of like building blocks. The resultant vertex configurations are classified by their energies determined by calculating partial overlaps in their dual images. A previously established hierarchy which took into account only pairs of tiles sharing a face is refined by calculating overlaps of higher orders, in particular, between triples sharing an edge.