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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.
Book Description
Magnus Wenninger gives an enthusiastic presentation of the complex set of uniform duals of uniform polyhedral shapes, many published here for the first time. Readers are shown, by photographs, line drawings, diagrams and commentary, how to make some of the author's models using index cards and glue.
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First Sentence
The five regular solids, also called the Platonic solids, are well known. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Back Cover
The five regular solids, also called the Platonic solids, are well known. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Back Cover
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4.0 out of 5 stars (1 customer review)
7 of 8 people found the following review helpful:
4.0 out of 5 stars
The companion to Polyhedron Models, 13 Jun 2000
By A Customer - Published on Amazon.com
This review is from: Dual Models (Hardcover)
While not as popular as his _Polyhedron Models_, Fr. Magnus Wenninger again provides a fascinating look into polyhedra, this time investigating the duals of the 75 uniform polyhedra. It is immediately evident why _Dual Models_ has not proven as popular--the reading level is significantly higher, as it is filled with detailed diagrams and plenty of mathematical background. The technical nature of dual polyhedra makes it much more difficult to explain, so it's understandable that this text lacks the same clarity and ease-of-approach that _Polyhedron Models_ did. Unfortunately, there isn't enough information provided to actually build all the examples--you'll have to do some of your own computation. Finally, the duals simply aren't as attractive or interesting as the uniform polyhedra, so the reader isn't as inclined to make models of them. But in the end, if you found _Polyhedron Models_ interesting, you'll also enjoy this book: they naturally complement each other.
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