Visualizing conjugation in affine Coxeter groups

Affine Coxeter groups are fundamental objects in mathematics and in crystallography. If two group elements are conjugate, then they have very similar algebraic and geometric properties. Using recent structural results of Milićević, Schwer and the second author, we develop an app to visualize conjugation in affine Coxeter groups in dimensions 2 and 3. The resulting pictures exhibit beautiful geometric symmetries.