Abstract The effects of the geometries of boron-rich solids on dynamical properties are discussed. Traditionally, it has been thought that the intericosahedral bond is stronger than the intraicosahedral bond. In the past, questions concerning this understanding have arisen, based on experimental results. Some of the apparent contradictions can be solved by considering the special geometries of the icosahedron-based structure. The geometrical concept is examined for elastic responses, librational modes, and anharmonic phenomena. An attempt has also been made to address the problem of the strength of the chain bond in boron carbides by ab initio calculations. Based on the present results, a model has been proposed to solve contradictions among experimental results.