Günter Ziegler (Freie Universität Berlin): The Realization Space of the 24-Cell.

Abstract:  If anyone will ever write “The BOOK of Examples”, then the 24-cell, discovered in the 18th century, will surely be one of its highlights: A self-dual regular polytope of dimension 4 with 24 vertices and 24 octahedra as facets, exceptional and unique in many respects…

The “realization space” of a type of polytope is the space of all correct sets of coordinates for this type. There are published proofs that all realization spaces of polytopes are manifolds, while the “universality theorem for polytopes” claims that this is far from the truth, that basically anything can happen, any semi-algebraic set occurs.

However, the examples that were constructed to prove this are very artificial – most polytopes that occur “in nature” (such as the 3-dimensional polytopes, simple polytopes, simplicial polytopes, etc.) have manifolds as realization spaces.

However, the 24-cell…

(Joint work in progress with Laith Rastanawi and Rainer Sinn.)

The event will be followed by the Reception held on Huxley Concourse Level 3. Registration in advance due to capacity restrictions by filling the form.