A ring of an even number of tetrahedra will flex in a pleasantly satisfying manner.

A video of the flexing of six stretched tetrahedra can be seen at: http://www1.ttcn.ne.jp/a-nishi/kaleidocycle/z_ani_kaleido.html

Here is the net for the ring of eight tetrahedra.

A good model can be make from moderately thin card. Each tetrahedron will be made from a single colour. The empty triangles should be hidden in the gluing. The final joining of the ring should be undertaken with sellotape or similar because there is some stressing involved in flexing.

One of the enrichment tasks on this site.
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