Hierarchy of vertices in imperfect icosahedral quasicrystals

Imperfect icosahedral quasicrystals are assumed to grow obeying a local rule which imposes the twin orientation of like building blocks. The vertex configurations and their representations are briefly discussed. The vertices are classified by their abundances and energies determined according to a simple model taking account of nearest-neighbour interactions and calculating the corresponding overlap volumes in dual space.