¶ Dymaxion Airocean World Map
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Dymaxion Airocean World Map:
"The article in LIFE did not describe any of the mathematical properties of my projection method. I am sure that you would be interested to have it pointed out that the triangular sections of my projection method represent those unique spherical triangles whose several vertexes are each coincident with a vertex of another identical triangle of a system of eight triangles, altogether forming a spherical triangular lattice of great circle arcs of 60° completely enclosing the sphere. This spherical triangular lattice (with equilateral spherical quadrangle interstices) represents the surface coincidence with a sphere of a unique system of tetrahedral segments of a sphere, all of whose apexes coincide at the center of the sphere. It happens that these particular equiangular spherical triangles of the infinite number between 180° and 60° are the only spherical triangles whose chords together with their interior vertexial radii form a united system of lines describing uniform, unit size, equilateral 60° triangles whose interior apexes coincide with the center of the sphere.
“There is no set of spherical triangles which uniformly subdivides all the surface of a sphere (as with the eight 90° equiangular triangles or the faces of an icosahedron) whose central”
