What is a kaleidocycle?

Take an even number of at least 6 equal regular tetrahedra. Two tetrahedra can be joined together to have one common edge. In this way first build a chain of all tetrahedra such that for every tetrahedron the two edges used for connexion are disjoint, then close this chain to build a ring. The result is a 3-dimensional object called a kaleidocycle (Greek: kálos [beautiful] + eîdos [form] + kyklos [ring]). In the case of at least 8 tetrahedra it has the interesting property that it can be turned through its center in a continuous motion.

The tetrahedra a kaleidocycle consists of need not neccessarily be regular. By using a certain class of suitable tetrahedra a great variety of different kaleidocycles (including twistible rings with 6 components) can be created.

In the book "M.C.Escher kaleidocycles" (1977) the mathematician Doris Schattschneider and the graphic designer Wallace Walker used some of the well known periodic drawings of the Dutch artist M.C.Escher to decorate kaleidocycles. They showed how to cover kaleidocycles continuously with repeating patterns (provided they have certain symmetry properties). It should be noted that in the work of Escher himself kaleidocycles do not appear.