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Icosahedrons are actually the basis for Spherical Quad Trees (SQT) used in computer science for spherical data. Every triangle can be easily split into four triangles of equal area. You have no special points like the poles or a split between 360° and 0° and so on. Each "Trixel" can be handled the same way as anyone else. You can also easily adapt these recursive splitting depending on the details you need.
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