A geometric realization of hyperbolic Coxeter groups

In the picture above, you can see a geometric realisation of the Coxeter group with presentation
as a reflection group acting on the hyperbolic plane in the Poincaré ball model. Different colored segments of the hyperplanes correspond to multiplication with different generators from the right. There is a bijection between elements in and tiles. The color of a tile indicates the reflection length of the associated group element, where the identity chamber is black.
This picture was created during the DAAD funded RISE Germany internship "Programming a geometric realization of hyperbolic Coxeter groups'' by Mireia Taus and Marco Lotz.
For more details and visuals, Marco Lotz explains this project along with the mathematics of hyperbolic space in a short presentation for the Heidelberg Experimental Geometry Lab here: