# Daniel Pellicer: Chiral 4-polytopes in space

Date: 5. 3. 2017

Source: Discrete mathematics seminar

Source: Discrete mathematics seminar

Torek, 7. 3. 2017, od 10h do 12h, Plemljev seminar, Jadranska 19

**Povzetek.
**In this talk we adopt the notion of skeletal polytope introduced by Grunbaum
in the second half of the 20th Century. A polygon is then a connected 2-valent
graph embedded in Euclidean space (no assumption on convexity or planarity),
and in general an *n*-polytope is a collection of (*n*-1)-polytopes satisfying
certain axioms. Such a structure is called chiral if it admits all possible
symmetry by abstract rotations, but none by abstract reflections.

Chiral polyhedra (polytopes of rank 3) were found and classified by Schulte only in 2005. Chiral 4-polytopes were claimed not to exist in 2004. This last claim was mistaken. In this talk we present the three chiral 4-polytopes in space.