This paper focuses on three groups of geometrical problems, closely related to material sciences in general and particularly to crystal/quasicrystal structures along with their formations and fullerenes. Some new results in mathematics are presented and discussed, for example, in section one, new estimates of minimum radius of local identity that guarantee that a Delone set is a point regular set. New results related to locally rigid packings are discussed in section two. One of the goals of the paper is to establish some internal (mathematically) and external (applications to material science) connections between research agendas of various studies in geometry and material sciences
