A new kaleidocycle set includes at least seven elements (tetrahedrons, for example), which are joined in a ring shape by means of rotating hinges. If tetrahedrons are used as exemplary elements, two ridge lines of each tetrahedron are joined to the corresponding ridge lines of an adjacent tetrahedron. Preferably, the plurality of tetrahedrons all have the same shape. However, two ridge lines of the tetrahedrons are "twisted". This means that the two ridge lines are not at right angles to one another, but are in a positional relationship rotated through a twist angle α relative to one another. The twist angle α is selected with an appropriate value such that the ring is closed (that is, such that the first element can be connected to the last element). The resulting ring has a single degree of freedom, and different faces can be exposed by manipulation in the same way as with a traditional kaleidocycle. However, the ring has a non-orientable topology, unlike a traditional kaleidocycle.
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