A metric graph (or Feynman graph) defines a positive semi-definite quadratic form via its Laplacian. The Voronoi cell associated to this quadratic form is an interesting polytope. We give a formula to determine the normal fan of the polytope from the graph. Computing the vectors that generate the fan is a crucial step when computing the tropical limits of Riemann theta functions, which show up in string theory when studying the alpha' expansion of worldsheet integrals at genus g>1. This is joint work with Hadleigh Frost.