Create mesh with vertices valency 3

I am trying to create a mesh of which each vertex has a valency of 3, i.e. that each vertex is connected to 3 other vertices. I have a starting surface which is curved, but the individual mesh faces that I want as a result are of course planar. I can make a hexagonal grid on the initial surface, but those hexagons are not yet planar (see image attached). Any suggestions?

I would use the planarize component of the nGon plugin for Grasshopper.