¶ All Space Filling: Octahedron and Vector Equilibrium
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Index Entry
We find that in closest packed spheres there are only two shapes spaces: what we call the concave octahedron and the concave vector equilibrium. . . . One is an open condition of the vector equilibrium and the other is a contracted one of the octahedron. So we begin to discover something fascinating, which is, if I take vector equilibria and contract them, as I showed you with internal-external octahedra, each one of those vector equilibrium packages, . . . we find that the triangular faces are occupying a position in closest packing of a space and the square faces are occupying the position of a sphere. Between them we had the internal and external octahedra; that is, the spaces between are either concave vector equilibria or concave octahedra. We could take the original vector equilibrium and bend the edges inwardly to make it concave or we could bend them outwardly and make spheres. In the first degree of contraction from vector equilibrium, it becomes a sphere or a space. If it bends inwardly it becomes spaces and if it bends outwardly they become spheres. We can then begin to call a space a concave vector equilibrium and we call a sphere a convex vector equilibrium, or we can call a space a concave octahedron which is one of the other kinds of transformations.
