  Describing the geometry of the dual amplituhedron without reference to a
particular triangulation is an open problem. In this note we introduce a new
way of determining the volume of the tree-level NMHV dual amplituhedron. We
show that certain contour integrals of logarithms serve as natural building
blocks for computing this volume as well as the volumes of general polytopes in
any dimension. These building blocks encode the geometry of the underlying
polytopes in a triangulation-independent way, and make identities between
different representations of the amplitudes manifest.
