Algorithm to generate Rhombic sphere tiling

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I want to make a function for generate generic Rhombic triacontahedron and any level of detail of rhombic sphere tiling

I want to know that can we use rhombic face to tile sphere in more detail than Rhombic triacontahedron? And how can we calculate the point or position of each?

Or is there any easier algorithm, such as try to make pair from the geodesic?