Math Pictures

This page provides some (interactive) mathematical illustrations (some of) which are related to my research.

The goal is that these pictures are also worth looking at for people without the right mathematical background, simply because they look cool :-). For everyone else there is also a short description what the depicted objects are.

(Note that you must have Java installed and enabled if you want to look at the pictures.)

Regular Polytopes

Beispiele für reguläre Polytope sind die fünf Platonischen Körper in Dimension 3. Die trivialen Beispiele Würfel, Simplex (= Tetraeder oder Dreieckspyramide in Dimension 3) und Kreuzpolytop (= Oktaeder in Dimension 3) gibt es in jeder Dimension (und ab Dimension 5 gibt es keine weiteren). In Dimension 4 gibt es außerdem drei weitere Beispiele.

Polytopes

Here are pictures of some interesting constructions.

Tropical Oriented Matroids (Toms)

If you are given a bunch of n usual (i.e., non-tropical) hyperplanes and a point in Rd then you can for each hyperplane determine on which side(s) of it the point lies. Now if you are given tropical hyperplanes then there are no longer two sides but instead d+1 sectors for every hyperplane. A tropical oriented matroid (tom) then describes the position of every point in Rd relative to each of our tropical hyperplanes. Toms can be visualised as mixed subdivisions of dilated simplices are by dual arrangements of tropical pseudohyperplanes.

Cubical Complexes

Misc