In 1985 Rosengren conjectured that the critical point of the symmetric, simple cubic (SC) Ising model is given by nu c identical to tanh(J/kBTc)= nu R identical to ( square root 5-2)cos( pi /8). This guess is examined in the context of attempting to construct the fully critical polynomial P3( nu x, nu y, nu z), with a root nu c (Jx, Jy, Jz) for the anisotropic SC Ising model with couplings Jx, Jy and Jz. It transpires that nu R is a surd which satisfies R( nu R2)=0, where R(x) is a quartic polynomial with integral coefficients; but R( nu 2) is a poor candidate for P3( nu , nu , nu ) since it does not display various `nice` properties embodied in the critical polynomial P2( nu x nu y) for the square, 2D Ising lattices. Methods for constructing nice polynomials Qk( nu x, nu y, nu z) that provide excellent approximations for nu c and for nu R are demonstrated. However, scaling arguments, etc., for the dimensional crossover induced when, say, Jz to 0 cast doubt on the existence and nature of the sought-for critical polynomial P3.