¶ Projective Transformation
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Index Entry
A two triangle system has neither insideness nor outsideness. I want to make a system which subdivides Universe into all the Universe inside the system and all the Universe outside the system. Now, I can take three triangles and I can put them together around one vertex and make the tetrahedron. A round each vertex there are always a minimum of “three triangles. I can insert a fourth triangle around each vertex and get the octahedron. I can next put a fifth triangle around each vertex and get the icosahedron. In this closed system there are 12 vertexes with five equilateral triangles around each vertex.” In a system "the largest number of triangles you can possibly have around a vertex is five. I can take that into the planar condition or the spherical, and in the spherical each of the corners will be 72°. Now that I find that I can get the total Earth’s surface on to the icosahedron, the edges of the icosahedron’s spherical triangles will all be 63° 26’. If possible, one of the things I want is to take the 12 vertexes of the icosahedron and manipulate them in such a way in relation to the sphere of the Earth that the vertexes always fall in the oceans.
