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The Et-Construction for Lattices, Spheres and Polytopes

Abstract

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 et al. We also construct for each d ≥ 3 an infinite family of (d – 2)-simplicial 2-simple d-polytopes, thus solving a problem of Grünbaum.

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Correspondence to Andreas Paffenholz or Günter M. Ziegler.

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Paffenholz, A., Ziegler, G. The Et-Construction for Lattices, Spheres and Polytopes. Discrete Comput Geom 32, 601–621 (2004). https://doi.org/10.1007/s00454-004-1140-4

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Keywords

  • Computational Mathematic
  • Face Lattice
  • Interesting Classis
  • Infinite Family
  • Cellular Sphere