equidistant mapping from icosahedron to sphere

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I am struggling to find an equidistant mapping that maps points from an icosahedron to a sphere, such that the points are spaced evenly (as much as possible) on the sphere.

A similar mapping from cube to sphere is described in this question, I'm looking for something similar to this. There is an old question where someone asks a mapping from an icosahedron to a sphere, but there no attempt is made to spread the points evenly.