A kaleidocycle is a closed chain of tetrahedra joined along opposite edges by hinges, forming a linkage that can turn inside out repeatedly (Schattschneider and Walker 1977, Schönke and Fried 2019). Each color identifies a tetrahedron, and the thick dark edges mark the hinges.
The classical six-hinged kaleidocycle illustrated above consists of six congruent tetrahedra with a 
angle between the two hinge
axes of each tetrahedron. In the ideal hinge model,
it has a single internal degree of freedom, meaning
that its shape can vary with a single parameter while
the tetrahedra remain rigid. A construction uses
isosceles tetrahedra with faces
that are congruent isosceles
triangles. If each such triangle has leg length 
and base length 
, with the bases serving as hinges, then
prevents a complete eversion
because neighboring tetrahedra collide (Schönke
and Fried 2019, pp. 90-91).
