¶ Foldability of Great Circles
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Index Entry
Foldability of Great Circles:
“Wave phenomena always being cyclic . . . I began to take whole circles. I could take four complete circles and fold them in such a manner as to make bow ties, and they fasten together and make the great circles. Everyone of the 25 and 31-- making a total of 56-- can be made by folding. You simply do your spherical trigonometry, your central angles. . . sometimes a four-part bow tie and sometimes a two-part bow tie. They go together and you can re-establish them, the biw ties together, corner-to-corner, and they make a whole sphere again and you can see the 15 great circles, you can see the 10 great circles, and so forth. . . They turn out to be only great circles. There’s no other way I can take a great circle and fold it, because everyone of the fundamental symmetries of both the icosahedron and the vector equilibrium are foldable into great circles where the energy instead of going cyclic around the whole system, can go around in a figure eight, for instance-- or it can go around in 15 great circles. In the 15 great circles you find they again disconnect and they go around very locally on the surface of the icosahedron. When you make up the icosahedron you find them in strange little curlicues and they’re very asymmetrical.”
