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Discrete & Computational Geometry

, Volume 32, Issue 4, pp 601–621 | Cite as

The Et-Construction for Lattices, Spheres and Polytopes

  • Andreas PaffenholzEmail author
  • Günter M. ZieglerEmail author
Article

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.

Keywords

Computational Mathematic Face Lattice Interesting Classis Infinite Family Cellular Sphere 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer 2004

Authors and Affiliations

  1. 1.Institut für Mathematik, MA 6-2, Technische Universität Berlin, D-10623 BerlinGermany

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