Centrally symmetric and balanced triangulations of S2×Sd−3

Generalized Heawood Numbers

“…The examples by Klee and Novik [32] of type S j ×S d−j realize equality in each of these inequalities with β j = 1 for j < d 2 and β k = 2 for d = 2k. For j = 2 also the examples of Wang and Zheng [58] realize equality. For β j = 0 (and fixed j) the inequalities are trivial but equality cannot be attained except for j = d 2 and the boundary of the cross polytope itself.…”