¶ Allspace Filling
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Index Entry
"If’ I put a little one-eighth octahedron in the corner of each of the eight triangular faces of the vector equilibrium it becomes a cube. Therefore, when I bring vector equilibria together in masses, it leaves a little space on each of these corners, but you remember that eight cubes always come together around one point. Therefore, there will be eight of these one-eighth octahedra on each of the corners which come together at this point. Therefore the eight of them together would make one octahedron. We find then that the vector equilibrium plus the octahedron on the outside of each of the triangular faces would fill all space.
When we bring the vector equilibria up to each other we find that two of their square faces match together. Within a square face we had a half octahedron, so that brings two of the square faces together and I get an internal octahedron between the two of them. The external octahedra are intervened between the vector equilibria on their triangular faces and there is an internal set of octahedra between the square faces."
