Let f be a polynomial of degree d with exactly n+4 monomial terms in R[x_1,…,x_n]. We show that one can efficiently compute an explicit polyhedral complex with the same isotopy type as the positive zero set of f. In particular, the complexity of our construction is polynomial in u + log d with high probability. Along the way, we derive and implement an algorithm that, given an n-variate (n+4)-nomial f, outputs a plot of the reduced A-discriminant contour in R^3.