FLOW LINES AND INTERRUPTED PROJECTIONS

I like the idea of having flow lines with length (or some other characteristic) associated with distance between items - particularly where spatial distortions occur. Buchin et al. (2014) seem to do this nicely.

Can we come up with flow lines that are sized according to great circle distances in the case of interrupted projections?

For example William-Olsson's equal-area star, Steinhauser's conoalactic, Fuller's dymaxion or the various cubic projections that exist.

Could we produce curves between points with length proportional to great circle distance, that maintained length as projection changes? 

HEXAGONS

I'd like a consistent plane to non-overlapping hexagons layout that does better than this one that Benjamin Hennig has produced for the ONS of UK parliamentary constituencies ...

http://visual.ons.gov.uk/visualising-your-constituency/