Packable hyperbolic surfaces with symmetries

TL;DR

This paper explores methods for packing hyperbolic surfaces with circles or horocycles, focusing on their symmetry properties and the implications for geometric configurations.

Contribution

It introduces new packing techniques for hyperbolic surfaces and analyzes their symmetry characteristics, expanding understanding of geometric packings in hyperbolic geometry.

Findings

Various packing configurations with circles and horocycles on hyperbolic surfaces

Observations on symmetry and asymmetry in these packings

Insights into the geometric structure of packings in hyperbolic spaces

Abstract

We discuss several ways of packing a hyperbolic surface with circles (of either varying radii or all being congruent) or horocycles, and note down some observations related to their symmetries (or the absence thereof).