Algebraic degrees of 3-dimensional polytopes

Results of Koebe (1936), Schramm (1992), and Springborn (2005) yield realizations of 3-polytopes with edges tangent to the unit sphere. We introduce two notions of algebraic degree for such constrained realizations and we compute them for some classes of polytopes. This is joint work with Michael Joswig and Marta Panizzut.