In this paper, we study slices of the parameter space of cubic polynomials,
up to affine conjugacy, given by a fixed value of the multiplier at a
non-repelling fixed point. In particular, we study the location of the $main\,
cubioid$ in this parameter space. The $main\, cubioid$ is the set of affine
conjugacy classes of complex cubic polynomials that have certain dynamical
properties generalizing those of polynomials $z^2+c$ for $c$ in the filled main
cardioid.
