Kaleidocycle

A kaleidocycle or flextangle is a flexible polyhedron connecting six tetrahedra (or disphenoids) on opposite edges into a cycle.

The kaleidocycle has an additional property that it can be continuously twisted around a ring axis, showing 4 sets of 6 triangular faces.

[citation needed] Because of this and their continuous twisting property, they are often given as examples of simple origami toys.

The kaleidocycle is sometimes called a flexahedron in analogy to the planar flexagon, which has similar symmetry under flexing transformations.

[1] Wallace Walker coined the word kaleidocycle in the 1950s from the Greek kalos (beautiful), eidos (form), and kyklos (ring).

The paper toy suggested how space and time could be folded to explain the magical travels of the story.