The type Cn root polytope P(C + n) is the convex hull in R n of the origin and the points ei − ej, ei + ej, 2e k for 1 ≤ i < j ≤ n, k ∈ [n]. Given a graph G, with edges labeled positive or negative, associate to each edge e of G a vector v(e) which is ei−ej if e = (i, j), i < j, is labeled negative and ei + ej if it is labeled positive. For such a signed graph G, the associated root polytope P(G) is the intersection of P(C + n) with the cone generated by the vectors v(e), for edges e in G. The… CONTINUE READING