Kinematics of the cuboctahedron
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 and consequently its vertices can be repositioned by folding (changing the dihedral angle) at 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.
| Kinematics of the cuboctahedron | |
|---|---|
Progressions between a cuboctahedron, pseudoicosahedron and octahedron. The cuboctahedron can flex this way even if its edges (but not its faces) are rigid. |
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