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


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.


Computational Mathematic Face Lattice Interesting Classis Infinite Family Cellular Sphere 
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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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