A note on this naming convention. In addition to triangles, flexagons can be made from squares, pentagons, hexagons and so on. The angles in the polygon can vary. The number of sides you can flex to can vary and is sometimes meaningless because flexing rearranges them so thoroughly. There are different strips you can use to make a flexagon with the same number of sides. You can even fold the same strip differently. Obviously you really canít encode all this information in a simple naming system.
The naming convention Martin Gardner used in his original Scientific American articles (and presumably drew from Stone, Tuckerman, Feynman and Tukey) was to use hexaflexagon when there were six equilateral triangles per side and tetraflexagon when there were four squares per side. Unfortunately this doesnít generalize very well. In Flexagons Inside Out, Les Pook simply used the name of the polygon, square flexagon, pentagon flexagon, etc. This seems like a good starting point in light of the variety out there.
More recently, octaflexagon and dodecaflexagon have been used to refer to triangle flexagons with 8 and 12 triangles per face respectively. Since triangles seem to work better than other polygons when you vary the number of polygons per face (due to the fact that flexagons that donít lie flat are harder to work with), it seems reasonable to use this as a general naming convention for triangle flexagons. This gives us tetraflexagon for four triangles, pentaflexagon for five and so forth.
Additionally, Iíve prefixed these names with the type of triangle used - equilateral, isosceles or right triangle. Using standard naming, you could then prefix this with the number of sides you can get to during flexing, e.g. trihexaflexagon, though I typically just refer to it as a 3-sided hexaflexagon. Many flexagons have flexings that mix up the faces. Additionally, odd-ordered flexagons like the pentaflexagon or heptaflexagon, donít have well defined sides since their flexings always mix up the faces. I may refer to these either by some secondary trait or by the number of unique faces it would theoretically have.
There are many terms for parts of a flexagon, some standard, some not. For example, the unfolded strip of paper goes by several names and I may refer to it as a strip, net or frieze. When folded, the flexagon consists of one or more stacks of polygons. Each of these stacks is called a pat. Each individual polygon is called a leaf. A folding or series of foldings that transforms the flexagon is called a flex. A face is what you see when the flexagon is in a standard position, with several polygons typically visible at once.
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