  We study a new discretization of the Gaussian curvature for polyhedral
surfaces. This discrete Gaussian curvature is defined on each conical
singularity of a polyhedral surface as the quotient of the angle defect and the
area of the Voronoi cell corresponding to the singularity. We divide polyhedral
surfaces into discrete conformal classes using a generalization of discrete
conformal equivalence pioneered by Feng Luo. We subsequently show that, in
every discrete conformal class, there exists a polyhedral surface with constant
discrete Gaussian curvature. We also provide explicit examples to demonstrate
that this surface is in general not unique.
