The word caleidocycle comes from the Greek(cali; beauty, eidos; form and cycle; ring, to turn or return to the point of origin).

A kaleidocycle is an articulated three-dimensional ring composed of pyramids joined at their edges. They can rotate about themselves indefinitely without breaking or deforming around their center.

Kaleidocycles are part of a discipline called 'Paper Architecture'. The best known examples are those formed by tetrahedra. The book M.C. Escher: Kaleidocycles, by Doris Schattschneider and Wallace Walker (Taschen publishing house) contains beautiful models decorated with Escher's tessellations for building.

According to the number of pieces, number of faces, edges and vertices, they are classified into different types and are called by a specific name. They can be hexagonal, octagonal, etc. and of order 4, 6, 8, etc.

If you want to try to make one, here you have some templates and instructions.

Exercises to download (click here)

Instructions for use (click here)

You can also create your own kaleidocycles here