|flex name||min order||min
|no. of pats
|bending or trimming|
|slot||5 (pentaflexagon)||5||yes||yes||all||trim tips|
|silver tetra||4 (tetraflexagon)||4||yes||no||4||no|
|pivot||4 (tetraflexagon)||3||no||>180° angle||4||no|
|pyramid shuffle||5 (pentaflexagon)||5||yes||yes||3||* no for 8+ (octaflexagon)
* trimming for 7 (heptaflexagon)
* bending for 5 & 6 (penta & hexaflexagon)
The above table lists a few of the many possible flexes you can use with various triangle flexagons.
The following shows examples of how a flexagon can change as a result of various flexes. All of these flexes apply to a wide variety of flexagons, so representative examples have been chosen. The left pair of polygons shows the front and back before the flex while the right pair shows the front and back after the flex. Dark gray shows which leaves were changed because of the flex. Light gray indicates that the same number is visible on the leaf, but the structure of the underlying pat (i.e. stacks of polygons) has changed.
These flexes help illustrate the difference between a global flex and a local flex. A global flex, such as the pinch flex, changes every pat in the flexagon. A local flex, such as the single flap flex, only changes some pats, while leaving others alone and the overall appearance unchanged (e.g. a hexaflexagon starts as a hexagon and ends as a hexagon). Others, such as the pocket flex (aka pyramid flex), are partial flexes that usually serve as components of other flexes.
See the Flex Notation page for a useful way to describe series of flexes. It shows how different flexes are related to each as well as interesting flex sequences.
|© Scott Sherman 2007||send comments to comments at this domain|