Euler's polyhedron formula applied to Kepler-Poinsot-polyhedra

25.10.2024, 11:00  –  Campus Golm, Building 9, Room 2.22 and via Zoom
Arbeitsgruppenseminar Analysis

Luisa Herrmann (Potsdam)

If one interprets the Kepler-Poinsot-polyhedra as the union of several objects and applies Euler's polyhedron formula on their number of vertices, edges and faces, than the result is two. This is also the case for normal connected polyhedra without holes. In my presentation I will explain how to interpret the Kepler-Poinsot-polyhedra as the union of several objects and how to count them. For that purpose, it is helpful to understand what a polygon, whose number of vertices is rational but not an integer could be. This makes it possible to apply Euler's polyhedron formula on the star polyhedra. Even though single polygons, whose number of vertices is not an integer, are not definable, one can count them as faces on two of the four star polyhedra. Therewith one gets the value two by applying Euler's polyhedron formula.

Wenn Sie digital an den Vorträgen teilnehmen möchten, wenden Sie sich bitte an Christian Molle molle @ uni-potsdam.de, um die Zugangsdaten zu erhalten.