The infinite polyhedra of Wachman, Burt, and Kleinmann

In 1974, three researchers at the Faculty of Architecture and Town Planning of the Technion produced a most amazing collection of isogonal polyhedra. Even more stunning was that the examples appear not to be mere drawings but instead photographs of physically created models for each polyhedron. They published their collection in the book Infinite Polyhedra, later reprinted in 2005. While it might be supposed the book was made in order to highlight what could become interesting architectural design elements, it is clearly a work of mathematics. But, very disappointingly, the book was overlooked by the mathematical community, or at least those interested in isogonal polyhedra. For example, this book was published three years before the much more widely known and cited (in terms of isogonal polyhedra) one by A.F. Wells. Branko discovered this book and showed it to me and I then wrote to the Technion asking where I could purchase one. However, Professor Wachman instead sent me a complimentary copy, for which I am most appreciative. It is my hope that the extraordinary efforts made by these three researchers, along with the students and staff at the Technion who helped them, will now see their discoveries made available to a much wider audience.

The book groups the polyhedra into sections according to their shaped appearances and these groupings are the same as used in the listings below on this page. The theory that was used for finding them was the same theory of nets that Wells used. The book begins with a preface that describes the overall structure of the book and includes some of the simpler polyhedra. The majority of the book then describes the more complex polyhedra. Thus the pages below that have Roman numerals refer to those polyhedra that appear in the preface section. Some pages have more than one polyhedron, and these are listed below as 't' or 'b', depending on whether they are on the top or bottom of the page. Polyhedra that have already appeared someplace else on some other web pages at this site are linked to those earlier appearances.

Because of the very large number of polyhedra in the book, in order to get them displayed on the Web as soon as possible they are shown here only as unlabeled ones. Eventually it is hoped they will be described along with all their labeled versions just like the other polyhedra on this site. Also, the list shown here at this time is incomplete because the remainder of the polyhedra are still being constructed. Because the book contains so many polyhedra this page is being posted while still unfinished with the missing VRML models to be filled in as they are completed.


The infinite polyhedra of Wachman, Burt, and Kleinmann



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Last updated: October 14, 2019