Constructions for 4-Polytopes and the Cone of Flag Vectors

2005/11/30 by Andreas Paffenholz, Paffenholz, Andreas, Axel Werner +1
Computer Science · Engineering · Mathematics · #52B05 #52B12 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #graph theory and CDMA systems #math.CO #msc:52B05 #msc:52B12

paper · pdf · doi:10.48550/arxiv.math/0511751

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

openalex publication_date 2005/11/30 · arxiv created 2006/07/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 g₂=0 on any number of n >= 13 vertices. In particular, this implies that the ray l₁, 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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