¶ Icosahedron (1)
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RBF Definitions
If we take the vector equilibrium with the center ball as the nucleus we can make a model of the 12 balls around one and put rubber bands between their centers. It is very easy to make a necklace of rubber bands of four great circles around together, the four great circles being the four great planes of the tetrahedron that went through the common center of vector equilibrium. When we have rubber bands it is possible to stretch the rubber band and pull the center ball out. We must remember that the vector equilibrium has six square faces and eight triangular faces. When we pull the center ball out these six square faces immediately rotate in such a manner that each of them becomes a diamond. Every one of the square faces become a diamond and the whole system becomes the icosahedron.
The balls simply rotate and contract a little. The center ball was keeping them from packing and so there is a little more compactibility when the center ball goes out.
Now we see omni-triangulation.and no more squares.
¶ Citations
- Oregon Lecture #7, p.293, 11 Jul’62
