Kinematics of the cuboctahedron

Unlike the cuboctahedron itself, the resulting system of edges and joints is rigid, and forms the vertex figure of the infinite tetrahedral-octahedral honeycomb.

The 12 vertices of the cuboctahedron spiral inward (toward the center) and move closer together until they reach the points where they form a regular icosahedron; they move slightly closer together until they form a Jessen's icosahedron; and they continue to spiral toward each other until they coincide in pairs as the 6 vertices of the octahedron.

The tensegrity icosahedron has a dynamic structural rigidity called infinitesimal mobility and can only be deformed into symmetrical polyhedra along that spectrum from cuboctahedron to octahedron.

Forcing the polyhedron away from its stable resting shape (in either direction) involves stretching its 24 short edges slightly and equally.

Force applied to any pair of parallel long edges, to move them closer together or farther apart, is transferred automatically to stretch all the short edges uniformly, shrinking the polyhedron from its medium-sized Jessen's icosahedron toward the smaller octahedron, or expanding it toward the larger regular icosahedron and still larger cuboctahedron, respectively.

In particular, the vertices always move in helices toward the center as the cuboctahedron transforms into the octahedron,[8][9] and Jessen's icosahedron (with 90° dihedral angles and three invariant orthogonal planes) is always the median point, stable to the extent that there is resistance to stretching or compressing.

Neither limit case is apt to apply perfectly to most real tensegrity structures, which usually have some elasticity in both the cables and the struts, giving their actual behavior metrics that are non-trivial to calculate.

[12] In engineering practice, only a tiny amount of elasticity is required to allow a significant degree of motion, so most tensegrity structures are constructed to be "drum-tight" using nearly inelastic struts and cables.