Constructions for 4-Polytopes and the Cone of Flag Vectors

Andreas Paffenholz, Axel Werner

Published 2005-11-30, updated 2006-07-14Version 2

We describe a construction for d-polytopes generalising the well known stacking operation. The construction is applied to produce 2-simplicial and 2-simple 4-polytopes with g_2=0 on any number of n >= 13 vertices. In particular, this implies that the ray l_1, described by Bayer (1987), is fully contained in the convex hull of all flag vectors of 4-polytopes. Especially interesting examples on 9, 10 and 11 vertices are presented.