CC BY-SA 4.0 UnportedGangl, Herbert2024-10-162024-10-162022https://oa.tib.eu/renate/handle/123456789/16851https://doi.org/10.34657/15873In this snapshot, we will first give an introduction to hyperbolic geometry and we will then show how certain matrix groups of a number-theoretic origin give rise to a large variety of interesting tessellations of 3-dimensional hyperbolic space. Many of the building blocks of these tessellations exhibit beautiful symmetry and have inspired the design of 3D printed jewellery.enghttp://creativecommons.org/licenses/by-sa/4.0/510Algebra and Number TheoryGeometry and TopologyReport