Icosahedral solids often command extreme strength, low mass density, good chemical inertness, and high thermal stability. These ceramic materials owe their mechanical performance to their networks of highly directional covalent bonding. Our work employs density functional theory to identify specific bonding characteristics that advantage these materials. We not only detail the ground-state configurations of virgin materials but also the evolution of bonding during hydrostatic compression. Particular focus is given to both boron suboxide and boron carbide because of their demonstrated potential for advanced applications.