Interplay between the structure and properties of new metastable carbon phases obtained under high pressures from fullerite C$_{60}$ and carbyne

A brief review of structural, electrotransport, optical, elastic, and mechanical properties of carbon phases synthesized under pressure by heating fullerite C$_{60}$ and carbynoid materials is given. A large variety of carbon modifications with a variable bonding type, a variable mean coordination number, a variable molecular or atomic structural type, a variable characteristic dimensionality (from zero-to three-dimensional structures), a variable degree of covalence, etc., were prepared. Emphasis in the review is given to the elucidation of the interplay between the structural and topological characteristics of carbon phases and their key electronic and mechanical properties. A version of the kinetic phase diagram of fullerite C$_{60}$ transformations on heating under pressure is also suggested. This version is modified with respect to the interpretations known in the literature.