Starting with one face as the "front", label the faces of an equilateral triangle tessellation with the corresponding face of regular icosahedron, as defined by adjacent faces. Many triangles will get more than one label. Prefer faces closer to the front as in breadth first search.
Yet another way to project a sphere onto a plane.
Cube, octahedron, tetrahedron also possible. And 4D to 3D.
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