Flexagons: Intro & Tetraflexagons, Part 1

My goal for this blog is to post at least one or two topics a week but sometimes life gets in the way. I spent a few weeks in August and September researching flexagons in order to put together the first of a two-part demonstration and workshop for my local bookarts study group. While flexagons are fun to play with as toys, they offer an unusual structure that can be used for text or images that mysteriously appear and disappear as their “pages” are turned.

To begin, flexagons are flat models made from folded strips of paper that can be flexed to reveal a number of hidden faces. There are two types of flexagons, flat and 3-dimensional. In this post I will be talking about the flat type.

In the flat group there are two types: four-sided (tetraflexagons) which are rectangular, usually square, in shape, and six-sided (hexaflexagons) which look like hexagons (these will be covered in another post). Depending on the template used and the folding pattern, flexagons can have three, four, five, six or more faces. Appropriate prefixes are added in front of the basic name to indicated how many faces. So, tetraflexagons become tri-tetraflexagons (3 faces), tetra-tetraflexagons (4 faces), penta-tetraflexagons (5 faces) and hexa-tetraflexagons (6 faces). Likewise, hexaflexagons become tri-hexaflexagons (3 faces), tetra-hexaflexagons (4-sided), etcetera.

As if the names weren’t confusing enough, a tetra-tetra-flexagon has several entirely different templates and folding patterns, so the name itself doesn’t tell us much about what type of flexagon it is, only that it has four sides and four faces. The most popular is based on the principle behind the 2000-year old Chinese toy called a Jacob’s Ladder and is sometimes called a magic book. Each face can have a different image or text that is revealed as one flexes the structure. Here is an article on how to make one.

This is a big topic, one which cannot be adequately covered in a few postings. If you get hooked, don’t be surprised if you find yourself spending hours of enjoyment (and sometimes frustration) as you try out the various structures and plot how to design on them.

Book credits (variations on Jacob's Ladder/Magic Book structure):
1st book, Jane Cheng, Baucis and Philemon (Ovid Met. 8.611-724) trans by artist
2nd book, c. j. grossman, Magic Book with Secret Panels