On the f-vectors of the pyramidal triangulations of point configurations
Valery N. Shevchenko, D. V. Gruzdev · Journal of Applied and Industrial Mathematics · 2009
A triangulation of a point configuration is called pyramidal if all its simplices have a vertex in common. A series of inequalities are derived for the components of the f -vectors of pyramidal triangulations, and, for every d ≥ 3, a d -dimensional convex polytope and its triangulation are constructed whose f -vector cannot be realized as the f -vector of a pyramidal triangulation.