Kaleidocycle


A kaleidocycle is a paper-folded model connecting 6 tetrahedra on opposite edges into a cycle. It can be constructed from a stretched triangular tiling net with 4 triangles in one direction and an even number in the other direction.
The model represents a flexible polyhedron that can be twisted around a ring axis, showing 4 sets of 6 triangle faces that can be drawn with different colors or patterns.

Example

Variations

Beyond 6 sides, higher even number of tetrahedra, 8, 10, 12, etc, can be chained together. These models will leave a central gap, depending on the proportions of the triangle faces.

History

Wallace Walker coined the word kaleidocycle in the 1950s from the Greek kalos, eidos, and kyklos.
In 1977 Doris Schattschneider and Wallace Walker published a book about them using M.C. Escher patterns.

Cultural uses

It was called a flextangle as a prop in the 2018 film A Wrinkle in Time, with its inner faces colored with hearts and patterns which hidden when those faces are folded together. The paper toy suggested how space and time could be folded to explain the magical travels of the story. The toy is given to the daughter by her father at the start of the movie and its hearts show how love can be enfolded and still there, even after the father mysteriously disappears.