Edited by Jane Rosemarin
  • Title: Folded Forms
  • Author: Alexander Heinz
  • Publisher: Schiffer Craft (August 28, 2023)
  • ISBN-13: 978-0-7643-6612-3
  • Binding: Hardback, sewn signatures
  • Pages: 176
  • Printing: Full color

I’ve been procrastinating over writing a review of this book for some time. The reason is that the method of folding isn’t new. That’s not to say, however, that Alexander Heinz didn’t independently discover it. Lewis Simon first published this folding method in “Modular Origami Polyhedra,” by Simon, Bennett Arnstein and Rona Gurkewitz, in 1989.1 I will concede, though, that when Simon discovered this module, he only published details of square and triangular versions, whereas Heinz has explored other polygons, comprising three types of triangular, five types of square, and pentagonal and hexagonal modules.

The book is nicely presented, with matte lamination on the cover, and thick, strong boards for the front and back covers and spine. It measures approximately 9¼ by 10½ inches, and is about ¾-inch thick, with a sewn signature binding (multiple signatures sewn together along the spine). This allows the book to lie flat when open, without damage to the spine. There are multiple bright pictures, diagrams and written instructions for each model. It’s typeset in a light variant of the Brandon Grotesque font, in 10 point, which makes a lowercase letter “o” approximately 1mm tall. Footnotes (indicated in the book by asterisks), are even smaller, in what appears to be 7-point text. See below for a more thorough explanation.2 I can see the artistic intent in leaving large areas of white space on pages with text, but in my opinion, this makes for difficult reading. To get a good feel for the layout of the book, I recommend having a look at a preview that the German publisher, Haupt Verlag, has uploaded to Issuu.

The book starts with the table of contents, listing 61 different models across eight chapters. Following the contents, there’s a preface and detailed introduction. Subsequent sections detail spatial structures and symmetries, practical considerations (cutting, folding and colors), an overview of the modules and a sample layout of a model page. The chapters that follow are each given a unique letter, and they separate the models based on the types of modules used. It’s worth noting that chapters start at “N” and work through to “U.” This is because chapters “A” through “M” are included in Heinz’s first book, “Folding Polyhedra,” which covers uniform polyhedra, whereas this second book covers other, less-uniform models.

The “Spatial Structures and Symmetries” chapter is a little confusing, as it mixes up the use of words to describe polyhedra, such as faces, edges and vertices, but I suspect this might have occurred in the translation from German to English.

Although the use of glue shouldn’t strictly speaking be necessary, the author does mention that you may like to use glue, particularly on the pentagonal and hexagonal modules. I’m inclined to think that glue may be required for larger models and also suspect this may be down to your choice of paper, the module size and the accuracy of paper preparation and folding.

I decided to fold a couple of models, one of an Octahedron (six square modules), which is shown in the introduction, and another, not included in the book, of a Rhombic Dodecahedron (six square and eight triangular modules).

Octahedron and Rhombic Dodecahedron. Both designed by Alexander Heinz and folded by Edward Holmes.

The appendices of the book cover didactic hints, a glossary, bibliography and image credits, about the author and acknowledgements.

To summarize, “Folded Forms” is a nicely presented book that contains a large selection of interesting polyhedra, each accompanied with clear photographs and written instructions. The models range from a handful of modules — six, for an Octahedron — to an 80-sided model comprising 132 modules. Folding the modules is relatively straightforward and shouldn’t pose too much difficulty, but the assembly of some of the more complex models may well prove somewhat more challenging.

This book is available worldwide through Amazon and covers the construction of many non-uniform polyhedra, including three Johnson Solids.

Endnotes

1. Rona Gurkewitz and Bennett Arnstein coined the term “gyroscoped” polyhedra, and have published works similar to these two-piece modules, made from single sheets. See: 3-D Geometric Origami: Modular Polyhedra (New York: Dover, 1989) ISBN-13: 978-0-486-28863-5 and “Multimodular Origami Polyhedra” (New York: Dover, 2003) ISBN-13: ‎978-0486288635. [back]

2. 10-point text is allocated a height of 10/72 of an inch (3.53 mm). However, no letter reaches to the top or bottom of this space. Since the x-height (the height of lowercase letters such as “x,” “a” and “o”) is different from font to font, the readability of same-size fonts will vary. If you want to learn more about typography and fonts, Google Fonts has a very good knowledge base and glossary on the subject. [back]

Editor’s Note: Endnote 1 was added on April 9, 2024 after Rona Gurkewitz pointed out the similarity in appearance between Heinz’s work and the designs in books of which she was a co-author.