It is surprisingly tricky to approximate a sphere by triangles in the sense of a complex. We do a sphere topology because it is the obvious initial condition and also because we know the answers and can check our computed potentials.

We use this logic to form an icosahedron and subdivide each of its faces into n2 equilateral triangles for some n≥1 about 4. This yields a simplex with 20n2 faces and 10n2+2 vertices. We move the vertices radially so that they all have distance 1 from the origin.

We follow this plan for recording the data of the configuration.

This is the code.