flexagon

OAB Definition

flat or three-dimensional structure with polygonal faces that is constructed from a strip or a specifically cut sheet of paper. This strip or sheet is folded into a shape made of stacked folds that expose different faces when the figure is flexed along its folds. Most are cyclical, ending where they begin.

Flexagons were discovered by mathematicians and are often viewed as recreational mathematics. Many resources about them are based in math and mathematical analysis. The book arts community has used them for some time because of their interesting movement and potential for narrative pacing and development.

There is disagreement about naming conventions. The most common are:

• [number of faces]-[polygons per face]-flexagon
• [number of faces]-[number of edges of overall shape]-flexagon
• A mix of colloquial names and descriptive terms.

Common flexagon names include trihexaflexagon (three faces, six sides and leaves), tetratetraflexagon (four faces, four sides and leaves), and the hexatetraflexagon (six faces, four sides and leaves). As a category or simplification they are often referred to as [shape]-flexagon. So, hexaflexagon and tetraflexagon.

Linked Terms