Centrally symmetric and balanced triangulations of S2×Sd−3

A small triangulation of the sphere product can be found in lower dimensions by computer search and is known in few other cases: Klee and Novik constructed a centrally symmetric triangulation of Si×Sd−i−1 with 2d+2 vertices for all d≥3 and 1≤i≤d−2; they also proposed a balanced triangulation of S1×Sd−2 with 3d or 3d+2 vertices. In this paper, we provide another centrally symmetric (2d+2)-vertex triangulation of S2×Sd−3. We also construct the...