Volumes of Polytopes Without Triangulations

Understand

The geometry of the dual amplituhedron is generally described in reference to a particular triangulation.

• A given triangulation manifests only certain aspects of the underlying space while obscuring others, therefore understanding this geometry without reference to a particular triangulation is desirable.
• In this note we introduce a new formalism for computing the volumes of general polytopes in any dimension.
• We define new "vertex objects" and introduce a calculus for expressing volumes of polytopes in terms of them.