I will explain the geometry of fully augmented link complements in the 3-sphere by looking at their link diagrams. I will show how to extend the method that was introduced by Thistlethwaite and Tsvietkova to fully augmented links and define a system of algebraic equations in terms of parameters coming from edges and crossings of the link diagrams. Combining this extension with the work of Purcell, I will show that the solutions to these algebraic equations are related to the cusp shapes of fully augmented link complements. As an application I will use the cusp shapes to study the commensurability classes of fully augmented links.

There will be a pretalk at 2 in the same room.