4 distributed points on a sphere by means of the Fibonacci spiral [4 points répartis sur une sphère à l'aide de la spirale de Fibonacci].

This set is far from the exact solution for the two sphere poles (obtained using the Fibonacci spiral) cannot be both vertices of the polyhedra.

See a set of 4 points generated by means of simulated annealing that gives a near perfect solution (a tetrahedron):

See some related pictures (including this one):


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