The number of cubes in an octahedron formed by stacking centered squares is a centered octahedral number, the sum of two consecutive octahedral numbers.
Regular cubes and octahedrons both have 12 edges, while regular icosahedrons have 12 vertices.
To be specific, to which of the five platonic solids—tetrahedron, cube, octahedron, and so on—is the ideal strawberry supposed to approximate?
Unfortunately, we now need to pack cycles into these modified octahedra, and for very short cycles we shall need to introduce several alternative modifications to the octahedra.
K (3) (2, 2, 2) is sometimes called the octahedron.
Repeat this process with a different octahedron for each of the paths until we run out of paths.
We shall then pack these trails of octahedra with cycles of arbitrary lengths.
We shall now modify the octahedra in the trail so as to include all the additional edges.
