thin king

The kaleidocycle, the name of a flextangle, is a paper toy. It is made by folding a piece of paper according to specific dimensions. It is shaped like a chain of six identical hollow triangular cones, connected side to side forming a ring. The base of two adjacent triangular cones may make contact such that it looks like a ring with three hexahedrons, or triangular bipyramids. And its outer circumference looks hexagonal.

The unique feature of this toy is that it can be turned around the circular axis of the ring. When it is being turned, inside out or outside in, all the pieces turn similarly simultaneously, And the beauty of this toy is that its pattern changes continuously while it is being turned. This is mesmerising, intriguing and captivating.

Additionally when the faces of the pieces are painted a plethora of changing colourful motifs come alive. Thus creativity is added to the enjoyment of this toy, and a challenge emerges for the design of the motifs. The design of the motifs is up to imagination, there is no boundary. This kaleidocycle is easy to make, yet it can offer so much fun, creativity and entertainment.

The creator of the flextangle is unknown, and it was Walter Walker who named it kaleidocycle. In 1977 Doris Schattschneider and Wallace Walker published a book about them using M.C. Escher patterns. And in 2018 researchers at the Okinawa Institute of Science and Technology Graduate University published a paper called Möbius kaleidocycles.

Where kaleidocycles are found, science, mathematics and art meet. Just as the nice looking wheel has had other applications by being eccentric, scientists foresee other applications by altering the structure of the flextangle, in its twist angle, the number of linkages and other characteristics. Researchers are now on the path that this kaleidocycle can spur advances in kinematics and robotics, in architecture and mechanics, in engineering and chemistry, and in creating new deployable devices.

This little kaleidocycle, the name of a flextangle, formed from Greek words meaning beauty, ring and cycle, may yet spawn great inventions. People ought to love and play toys.