# Combinatorics Seminar 2015

Date: Mon, Jan 4, 2016

Time: 12:45 - 13:45

Venue: Middle Meeting Room

Title: Scribability problems for polytopes

Abstract:

In 1832 Steiner asked about the existence of non-inscribable 3-dimenional polytopes. The first example was not given until nearly 100 years later by Steinitz. Then the scribability problem is generalized to higher dimensions, and several weakened versions are proposed. In this talk, we propose a new variation, namely the $(i,j)$-scribability problem, in strong and weak forms. Roughly speaking, we wonder: can every $d$-dimensional polytope be realized with all the $i$-faces "outside" the sphere, but all the $j$-faces "intersect" the sphere? We managed to give answers to most cases. The $(i,j)$-scribability is interesting in its own right, and also helpful for classical scribability problems. In particular, we obtain complete answer to the classical scribability problem for stacked polytopes and cyclic polytopes.

This is joint work with A. Padrol.

Slides: View slides

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