Date started: 2019

Leads: Max Krause and Tashrika Sharma

### Abstract

The figure-eight knot is the simplest hyperbolic knot, meaning that its complement can be given a complete hyperbolic metric. A way to see this is to split the complement into two ideal tetrahedra.

The goal of this project is to show how two such tetrahedra should be glued together in order to obtain the figure-eight complement. The first lead is uses 3D rendering software to create an animation of the gluing, whereas the second lead focuses on creating schematic diagrams to highlight the steps in the gluing process.

### Media

### References

- William P. Thurston:
*The Geometry and Topology of Three-Manifolds*(2002)