Extended Icosahedral Structures discusses the concepts about crystal structures with extended icosahedral symmetry. This book is organized into six chapters that focus on actual modeling of extended icosahedral crystal structures. This text first presents a tiling approach to the modeling of icosahedral quasiperiodic crystals. It then describes the models for icosahedral alloys based on random connections between icosahedral units, with particular emphasis on diffraction properties. Other chapters examine the glassy structures with only icosahedral orientational order and the extent of translational order in such structures relates to the nature of their growth. Lastly, the use of the polytope concept to rationalize and construct real structures with varying degrees of icosahedral order is addressed. This book is of great value to physicists, crystallographers, metallurgists, and beginners in the field of quasicrystals.