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 Coxeter Polyhedra
- Page III: the {4,6} sponge
- Page III: the {6,4} sponge
- Page III: the {6,6} sponge

- Cylindrical Infinite Polyhedra
- Page VIII: {4,4} prismatic rods with various polygonal cross-sections
- Page VIII: {3,6} antiprismatic rods with various polygonal cross-sections
- Page VIII: 3.3.3.4.4 rods made with alternating prisms and antiprisms
- Page VIII: {3,6} rods with square, hexagonal, and octagonal cross-sections
- Page VIII: 3.3.3.4.4 rods (longitudinal strips of squares and triangles)
- Page VIII: {3,6} helicoid rods with various polygonal cross-sections

- Corrugated Polyhedra
- Page IX: {4,4} folded planes (two kinds)
- Page IX: {3,6} folded planes (two kinds)
- Page IX: 3.3.3.4.4 folded planes (three kinds)

- Mono-Layered Polyhedra
- Page 2 (t,b): Two (S2 and N5) of the fifteen {4,5} lattice grid polyhedra
- Page 3 (t): A 4.4.8.8 slab polyhedron
- Page 3 (b): A 4.4.4.8 slab polyhedron
- Page 4: A 3.3.4.3.4.4 slab polyhedron
- Page 5 (t): A 3.3.3.3.3.4.4 slab polyhedron
- Page 5 (b): A {3,8} slab polyhedron
- Page 6: A 4.4.6.6 slab polyhedron
- Page 7: A 4.4.12.12 slab polyhedron
- Page 12 (t): A 3.3.6.3.4.4 slab polyhedron

- Multi-Layered Polyhedra
- Page 15: Polyhedron S3 of the {4,5} lattice grid polyhedra
- Page 16: Polyhedron N7 of the {4,5} lattice grid polyhedra
- Page 17: Polyhedron N11 of the {4,5} lattice grid polyhedra
- Page 18: A 4.4.8.8 multi-layered polyhedron
- Page 19: A 4.4.4.8 multi-layered polyhedron
- Page 20: A {4,5} multi-layered polyhedron
- Page 21: A 3.3.4.3.4.4 multi-layered polyhedron
- Page 22: A 4.3.3.4.4.3.4 multi-layered polyhedron
- Page 25: Polyhedron (3
^{9})P_{11}of the Hughes Jones polyhedra - Page 26: Polyhedron (3
^{9})P_{2}of the Hughes Jones polyhedra - Page 27: A 4.3.4.4.3.3.3.4 multi-layered polyhedron
- Page 35: A second 4.3.4.4.3.3.3.4 multi-layered polyhedron
- Page 39: A 4.4.6.4.4.6 multi-layered polyhedron
- Page 40: A 4.4.4.4.6 multi-layered polyhedron
- Page 42: A 4.3.3.6.3.4 multi-layered polyhedron
- Page 50: Polyhedron N6 of the {4,5} lattice grid polyhedra
- Page 51: Polyhedron N12 of the {4,5} lattice grid polyhedra

- Multi-Directional Polyhedra
- Page 67: The {4,6} Coxeter sponge
- Page 68: The {6,4} Coxeter sponge
- Page 76: The {6,6} Coxeter sponge
- Page 83: Polyhedron (3
^{9})P_{1}of the Hughes Jones polyhedra - Page 87: Polyhedron S1 of the {4,5} lattice grid polyhedra
- Page 96: A 4.4.8.8.4 multi-directional polyhedron
- Page 98: A 4.4.4.8 multi-directional polyhedron

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