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The $E_t$-Construction for Lattices, Spheres and Polytopes

Andreas Paffenholz·Günter M. Ziegler
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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, Kuperberg and Ziegler. We also construct for each $d\ge3$ an infinite family of $(d-2)$-simplicial 2-simple $d$-polytopes, thus solving a problem of Grünbaum.

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Andreas Paffenholz, Günter M. Ziegler. 2004-03-17. The $E_t$-Construction for Lattices, Spheres and Polytopes. https://arxiv.org/abs/math/0304492

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