¶ Prime Structural Systems
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Index Entry
"We find there are only three possible omnitriangulated systems that subdivide Universe. There are the three faces around one vertex which is the tetrahedron; the four faces around one vertex which is the octahedron; and the five faces around one vertex which is the icosahedron.
You can’t have six because it would be flat and would not come back on itself to close the system. It would be neither concave nor convex. We have the positive and negative condition of these three things. Remember that you cannot have a polygon of less than three sides. So the triangle is minimum polygon; it is the only polygon that is inherently stable. We have learned that the triangle stabilizes itself with minimum effort, so we learn that triangulated systems are the systems of the least effort. If they are equilateral triangles then all the system is of equal effort in all directions… so that there are only three possible cases: tetrahedron, octahedron, and icosahedron."
¶ Citations
- Oregon Lecture #7, p.249, 11 Jul’62
