2003/04/30 by Andreas Paffenholz, Günter M. Ziegler, Paffenholz, Andreas +1
Mathematics · #06A07 #52B11 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG) #math.CO #math.MG #msc:06A07 #msc:52B11
paper · pdf · doi:10.48550/arxiv.math/0304492
21 pages, many figures
arxiv created 2004/03/17 · arxiv updated 2009/11/30
We describe and analyze a new construction that produces new Eulerian lattices from old ones. It specializes to a construction that produces new strongly regular cellular spheres (whose face lattices are Eulerian). The construction does not always specialize to convex polytopes; however, in a number of cases where we can realize it, it produces interesting classes of polytopes. Thus we produce an infinite family of rational 2-simplicial 2-simple 4-polytopes, as requested by Eppstein, Kuperberg and Ziegler. We also construct for each d≥3 an infinite family of (d-2)-simplicial 2-simple d-polytopes, thus solving a problem of Grünbaum.