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An enthusiastic presentation of the complex set of uniform duals of uniform polyhedral shapes.
In Dual Models, written in the same enthusiastic style as its predecessors Polyhedron Models and Spherical Models, Magnus J. Wenninger presents the complete set of uniform duals of uniform polyhedral, thus rounding out a significant body of knowledge with respect to polyhedral forms. He begins with the simplest convex solids but then goes on to show how all the more difficult, non convex, uniform polyhedral duals can be derived from a geometric theorem on duality that unifies and systematizes the entire set of such duals. Many of these complex shapes are published here for the first time. Models made by the author are shown in photographs, and these, along with line drawings, diagrams, and commentary, invite readers to undertake the task of making the models, using index cards or tag paper and glue as construction materials. The mathematics is deliberately kept at the high school or secondary level, and hence the book presumes at most some knowledge of geometry and ordinary trigonometry and the use of a scientific type small electronic calculator. The book will be useful as enrichment material for the mathematics classroom and can serve equally well as a source book of ideas for artists and designers of decorative devices or simply as a hobby book in recreational mathematics.
Table of content:
Foreword John Skilling; Preface; Introduction; 1. The five regular convex polyhedra and their duals; 2. The thirteen semiregular convex polyhedra and their duals; 3. Stellated forms of convex duals; 4. The duals of nonconvex uniform polyhedra; 5. Some interesting polyhedral compounds; Epilogue; Appendix; References; List of polyhedra and dual models.
In Dual Models, written in the same enthusiastic style as its predecessors Polyhedron Models and Spherical Models, Magnus J. Wenninger presents the complete set of uniform duals of uniform polyhedral, thus rounding out a significant body of knowledge with respect to polyhedral forms. He begins with the simplest convex solids but then goes on to show how all the more difficult, non convex, uniform polyhedral duals can be derived from a geometric theorem on duality that unifies and systematizes the entire set of such duals. Many of these complex shapes are published here for the first time. Models made by the author are shown in photographs, and these, along with line drawings, diagrams, and commentary, invite readers to undertake the task of making the models, using index cards or tag paper and glue as construction materials. The mathematics is deliberately kept at the high school or secondary level, and hence the book presumes at most some knowledge of geometry and ordinary trigonometry and the use of a scientific type small electronic calculator. The book will be useful as enrichment material for the mathematics classroom and can serve equally well as a source book of ideas for artists and designers of decorative devices or simply as a hobby book in recreational mathematics.
Table of content:
Foreword John Skilling; Preface; Introduction; 1. The five regular convex polyhedra and their duals; 2. The thirteen semiregular convex polyhedra and their duals; 3. Stellated forms of convex duals; 4. The duals of nonconvex uniform polyhedra; 5. Some interesting polyhedral compounds; Epilogue; Appendix; References; List of polyhedra and dual models.