Dual Models by Magnus J. Wenninger (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I get overly enthusiastic about this subject and this book just stokes that fire. Reference it frequently just as food for thought. It gives a great coverage of dual model basics in a straightforward and easy to follow way. The text is complemented well with visual imagery. Great book.

⭐For fifty years this reviewer has made and loved polyhedra: from the original volumes like Cundy & Rollett’s classic “Mathematical Models”and Coxeter’s “Regular Polytopes”, via Wenninger’s “Polyhedron Models”, to Holden’s, “Shapes, Spaces & Symmetry”. Particularly usefulfor model makers is “Polyhedron Models” (though some drawings, be warned, have minor errors, and why on earth couldn’t he classify hisnon convex polyhedra in a more logical order? – semi-regular first, cubic symmetry next, dodecahedral next etc). “Dual Models” is finefor us model makers, the details & plane faces are there, and I much appreciated the introduction to the concept of infinite stellations, butthe archimedian duals should have had TWO photos rather than one confusing super-imposed photo.The quality of the photos is a disgrace, not just to this century but to 1960 or so! Shame on the Cambridge University Press! – they decidedobviously that this book would not be a good seller, so gave it to a temporary clerk or skimped with low quality. Not worthy of a greatuniversity, and I shall examine their publications closely in future – they rather lost my trust!! And is it REALLY too much trouble to have some coloured photos in this day and age? Imagine how wonderful Wenninger’s books would look like with coloured photos (This reviewerdoes not need to – I glued my own over theirs!). The difference would be like between a 1920 film and a (James Cameron, say) 2010 film!And the book refers to “Polyhedron Models” so often that I almost wondered why publish it separately! The author should alsohave NAMED the model whose dual he is illustrating. (which I have done in my copy). So “Duals” is simply is not in the same class as “Polyhedron Models”.except for experienced and keen model makers. Four stars to Wenninger for his really good service to usall with his two books, no stars to Cambridge University Press for their niggardly meanness in quality.

⭐Full of beautiful geometric constructs, an exhaustive book which tells you all you need to know about the topic. More colour images would have been helpful

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