  We find an explicit matrix model computing the refined topological vertex,
starting from its representation in terms of plane partitions. We then find the
spectral curve of that matrix model, and thus the mirror symmetry of the
refined vertex. With the same method we also find a matrix model for the strip
geometry, and we find its mirror curve. The fact that there is a matrix model
shows that the refined topological string amplitudes also satisfy the
remodeling the B-model construction.
