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The skeleton of a cuboctahedron, considering its edges as rigid beams connected at flexible joints at its vertices but omitting its faces, does not have structural rigidity. Consequently, its vertices can be repositioned by folding (changing the dihedral angle) at the edges and face diagonals. The cuboctahedron's kinematics is noteworthy in that its vertices can be repositioned to the vertex positions of the regular icosahedron, the Jessen's icosahedron, and the regular octahedron, in accordance with the pyritohedral symmetry of the icosahedron.[1][2]
- ^ Gunn & Sullivan 2008, §3. Pyritohedral Symmetry; "The pyritohedral 3D symmetry group is the unique polyhedral point group that is neither a rotation group nor a reflection group."
- ^ Koca et al. 2016, p. 145, 4. Pyritohedral Group and Related Polyhedra; see Table 1.