A geometric framework (G, p) in the d-dimensional Euclidean space is globally d-rigid if the placement p is unique up to isometric transformations. In the generic case, global d-rigidity is a graph property. Similarly to d-rigidity, global d-rigid graphs have been understood when d=1 or d=2, while no such characterization is known for d>2. Hence, research has naturally focused on special cases, such as (partially) triangulated surfaces. In 2019, Jordan and Tanigawa showed that every 4-connected triangulation of the projective plane is globally rigid.

In this talk, we shall discuss recent results in global 3-rigidity on (partially triangulated) projective planar graphs.

This is joint work with Sean Dewar and Anthony Nixon.