octahedron betydelse and definition

Exempel på octahedron

• 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.