The simplest kaleidocycle is a ring of an even number of tetrahedra. (Tetrahedra are pyramids with equal edges and equilateral triangles as sides.) The tetrahedra are connected on perpendicular edges. What makes it special is that you can continually twist it inwards or outwards while it shows different sides of each tetrahedron. There is an infinite number of kaleidocycles. The tetrahedra becomes