Here is a quick node program, and the blue source circular conformal mesh of planar, non-regular symmetric hexagons, which conformally maps to a sphere, using sterographic projection.

The hexagons are not regular hexagons. They have certain cross ratio properties. More to come.

This script is based upon the paper "Conformal hexagonal meshes" by Christian Muller, available here: https://www.dmg.tuwien.ac.at/geom/ig/publications/oldpub/2011/hexa/paper_docs/hexa.pdf

This 2d mesh was constructed by hand. I plan to make a node to create the 2d meshes.

- Brian

The sphere is open at the poles, and is not centered on the equator. Using a correct radius should center the hexes on the equator...