I remember seeing something similar to https://www.jasondavies.com/maps/voronoi/capitals/. But the areas were weighted by the populations of the capitals. You ended up with something quite close to real political maps IIRC.

The first thing I noticed was the spherical dodadecahedron and if you turn on Delaunay triangulation, then it's dual the icosahedron. The latter being my favourite polyhedron, although our relationship is entirely platonic.

It would be fun to do Turtle graphics along geodesics on the sphere. If one adds Loxodromic paths to the Turtle, even better.

The geodesic turtle on the globe would be a good way to play with other platonic solids.

Beautiful :)

The idea that springs to my mind is to do Delaunay and Voronoi using spherical geometry. I think the article uses flat Euclidean geometry but if we tweak the fifth axiom we could do spherical or hyperbolic?