Fold lines of type 1 triangles. The springiness of tensegrity structures occurs in the hinging along the fold lines.
Type 1 triangles occur always in pairs. The fold line of each wing-pair of triangles is similar to a crease in the folded-paper column to the right.
Kite frame structure with its two struts and four tension lines is composed of type 1 triangles. Type 1 triangles occur here also in pairs making a diamond form. In the kite frame, two face-to-face diamonds share the tension lines on opposite faces of the kite. Note that this most economical of structures is actually a flattened tetrahedron.
This folded paper column simulates the geometry of a three-way tensegrity column. The type 1 triangles are red and the type 2 are in green.
Unlike tensegrity, this paper fascimile is not a prestressed structure. Still, it seems likely that the valley and hill folds even of randomly crinkled paper bear a close relationship to tensegrity’s tension and compression patterns of forces.