On a partition of a convex polytope into simplexes without new vertices (Q1282488)

The author considers the \(f\)-vectors (sequences of numbers of faces) of triangulations of convex (particularly simplicial) polytopes which use only their vertices. However, much of what is proved here is already known, or easily deduced from earlier results. For example, the relationships among numbers of interior and boundary faces are dealt with by the reviewer and \textit{D. W. Walkup} [Mathematika, Lond. 18, 264-273 (1971; Zbl 0233.52003)], and triangulations of cyclic polytopes have been extensively investigated in recent years. The translation from the Russian is also infelicitous, and uses terms foreign to the subject (``adjacentive'' for ``neighbourly'' is an especially horrible instance).