Visualization of sphere and horosphere packings related to Coxeter tilings generated by simply truncated orthoschemes with parallel faces

Abstract

In this paper we describe and visualize the densest ball and horoball packing configurations belonging to the simply truncated 3-dimensional hyperbolic Coxeter orthoschemes with parallel faces using the results of [46]. These beautiful packing arrangements describe and show the very interesting structure of the mentioned orthoschemes and the corresponding Coxeter groups. We use for the visualization the Beltrami-Cayley-Klein ball model of 3-dimensional hyperbolic space H 3 and the pictures were made by the Python software.