This workshop will focus on transformations of icosahedra and their applications to material growth. Starting from the observations that an icosahedron can be transformed into various other shapes by changing angles between bonds, but not the length of bonds, we will explore the mathematics of these transformations (e.g. how can these transformations be described and categorized), as well as applications to material growth. This workshop will include several mathematicians (both analytic and algebraic), physicists (including crystallographers who have worked on icosahedral crystals) and chemists who will be involved in this effort. Some of these ideas have been considered earlier by Buckminster Fuller, Alan MacKay and Maroon Tabbal, but we believe that we can further develop this in both the directions of mathematics and applications.