In this context, the cube is a hexacatenane, and the truncated octahedron is a 14-catenane.
Our strategy is to pack cycles into sequences of linked octahedra.
We therefore need to allow some 'overflow' from one octahedron to the next.
The tetrahedron, the octahedron and the cube may all be related to the diameter of the circumscribing sphere with lengths which are 'commensurable in square'.
For the octahedra this is at most 5.
We shall construct the packing one octahedron at a time, so that at each step we may have some incompletely packed cycles.
We may also have missed at most 34 x 4 squares and triangles when we changed back some octahedra.
We shall now modify the octahedra in the trail so as to include all the additional edges.
