  The paper deals with cubic 1-variable polynomials whose Julia sets are
connected. Fixing a bounded type rotation number, we obtain a slice of such
polynomials with the origin being a fixed Siegel point of the specified
rotation number. Such slices as parameter spaces were studied by S. Zakeri, so
we call them \emph{Zakeri slices}. We give a model of the central part of a
slice (the subset of the slice that can be approximated by hyperbolic
polynomials with Jordan curve Julia sets), and a continuous projection from the
central part to the model. The projection is defined dynamically and is
coherent with the dynamical-analytic parameterization of the Principal
Hyperbolic Domain by Petersen and Tan Lei.
