Constructions for 4-Polytopes and the Cone of Flag Vectors

Details Constructions for 4-Polytopes and the Cone of Flag Vectors Constructions for 4-Polytopes and the Cone of Flag Vectors

2005-11-30

arxiv.org/abs/math/0511751v2

Mathematics

Combinatorics

20 pages, 18 figures; minor corrections and changes in notation, added reference

Scientific paper

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.

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