Triangulated 3-polytopes without faces of low weight

In this note, precise upper bounds are determined for the minimal degree-sum w of the vertices of a face in several classes of triangulated 3-polytopes in terms of the maximal length of a path consisting of 4-vertices. In particular, if no two 4-vertices are adjacent, then w ⩽ 37, and if no 4-vertex is adjacent to a 3- or 4-vertex, then w ⩽ 29.