We will discuss two topics relevant to this workshop: (1) A general framework for convergence of discrete conformal mappings is given that works for a wide variety of discrete conformal structures and on general Riemannian surfaces. This framework is a direct generalization of the framework of the proof of Rodin-Sullivan together with Z. He/He-Rodin’s work on convergence of the derivative of circle packing maps. The proof utilizes Riemannian barycentric coordinates and axiomatizes a generalization of hexagonal rigidity. (2) The finite volume Laplacian that appears in discrete conformal variations of angles is studied on a single simplex in all dimensions. The determinant of this operator in two dimensions has had a geometric interpretation for some time, and we will look at the generalization of this formula to a Euclidean simplex in any dimension with arbitrary choice of orthogonal dual structure. Connections of this work to the linear algebra of spheres/hyperplanes as points in Minkowski space will be emphasized.