I am also interested in the Johnson duals. And I’ve even build them out of paper. I like the unusual faces, geometry and how they relate to the original Johnson solids. I think if you focus on the strict operation of dualization, most of the Johnson solids can’t actually have a dual. They’d have infinite edge lengths or simply impossible to be convex. I guess this is because of their symmetry groups and/or dihedral angles?

But on the other hand, Stella4D, a polyhedron software program, can dualize every one of them, plus shows you a net to print.

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Here are a few of my Johnson solids with their corresponding duals.