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

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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.
21 pages, many figures

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Metric Geometry, Combinatorics, 52B11, 06A07

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http://salesiana.dossiersoluciones.com/handle/123456789/67318

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0304492
 http://arxiv.org/abs/math/0304492

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arXiv