Kaleidocycles are a mechanical toy featuring a number of tetrehedra chained together to form a loop which can be rotated in on itself. They were popularised and named by Wallace Walker in the 1950s; and have continued to show up in media and museum gift shops ever since.

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What are they?

A tessellation is a set of figures which can cover the plane indefinitely. A hinged tessellation is a set of figures which not only cover the plane indefinitely, but has a set of hinges such that each figure can rotate about …