Of Play, Sisterhood, and the HEXA-DODECA-FLEXAGON

In her article "Flexagon Fever," Ela Schwartz pretty much explains all you need to know about the nature and allure of the flexagon. She writes:

"What is a flexagon, you ask? At first glance it looks innocuous enough, like a folded hexagon or square, a child's fortune teller or cootie catcher, or a piece of origami. But look closely and you'll see hidden layers lurking between the front and back. When you fold or pinch corners together, the flexagon 'flexes,' meaning a formerly hidden layer will come to light as the top layer folds underneath."

In a subsequent sister, Ela's sister, Ann Schwartz, writes about her discovery of the HEXA-DODECA-FLEXAGON, which, she explains,

"...flexes into totally new shapes in its flattened positions. One is a hexagon in which the triangles are arranged in a nonradial fashion. The other is what can be described as a triangle-shaped propeller: a large triangle with smaller triangles arranged around it. The hexa-dodeca flexagon also naturally combines triangles from its basic faces to produce a number of hybrid faces, all this with proper flexing, no twisting or pulling. And the flexagon has what I call 'rogue' triangles, a pair of triangles that swing along 1 hinge; the triangles are not attached to the flexagon on all 3 sides. Oddly enough, even when these triangles are not lying in what one would consider the right position, the hexa-dodeca still flexes smoothly."

For those of us who share fascination in the ever unfolding mysteries of fun, Ela and Ann's delight is infectiously validating, no matter how many sides or shapes their toys of wonder embrace.