The E_t-construction for lattices, spheres and polytopes

Andreas Paffenholz and Günter M. Ziegler— 2004

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 Gr\"unbaum.

TitelThe E_t-construction for lattices, spheres and polytopes
VerfasserAndreas Paffenholz and Günter M. Ziegler
Erschienen inDiscrete & Computational Geometry (Billera Festschrift: M. Bayer, C. Lee, B. Sturmfels, eds.), volume 32, pages 601-624