In the Epilogue of my book Polyhedron models I mentioned that none of the Archimedean duals had been presented and also that the stellation process described in that book for two of the regular polyhedra and for the two quasi-regular solids can be applied to any of the other Archimedean polyhedra, as well as to all their duals. In my book Spherical models I extended the techniques of model making to the modeling of spherical polyhedra, going thereby into a deeper presentation of the mathematical basis for polyhedral symmetry. This book, Dual models, now completes a significant body of knowledge with respect to polyhedral forms.

In this book I propose to follow the same style as that used in the two earlier ones, presenting models in photographs, along with line drawings, diagrams, and commentary. You will find here not simply a multiplication of geometric forms but an underlying mathematical theory that unifies and systematizes the whole set of duals of uniform polyhedra. Some of these models are not as complex as some of those in the first book. Also, the mathematical approach to geometrical forms used in the second book is brought into very practical application here. So I can assure you that the level of mathematics you will need in order to follow the details of drawing and calculation will remain at the high school or secondary level.