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In this short communication, we observe that the Graphical Traveling SalesmanPolyhedron is the intersection of the positive orthant with the Minkowski sumof the Symmetric Traveling Salesman Polytope and the polar of the metric cone.This follows almost trivially from known facts. There are two reasons why wefind this observation worth communicating none-the-less: It is very surprising;it helps to understand the relationship between these two important families ofpolyhedra.

A note on the relationship between the Graphical Traveling Salesman Polyhedron, the Symmetric Traveling Salesman Polytope, and the Metric Cone