Complex 1-variable polynomials with connected Julia sets and only repelling
periodic points are called \emph{dendritic}. By results of Kiwi, any dendritic
polynomial is semi-conjugate to a topological polynomial whose topological
Julia set is a dendrite. We construct a continuous map of the space of all
cubic dendritic polynomials onto a laminational model that is a quotient space
of a subset of the closed bidisk. This construction generalizes the "pinched
disk" model of the Mandelbrot set due to Douady and Thurston. It can be viewed
as a step towards constructing a model of the cubic connectedness locus.