A new map preojection
I found this on Facebook today. It is a new, and very unusual, map projection that greatly reduces distortion.
http://all-that-is-interesting.com/authagraph-world-map
http://all-that-is-interesting.com/authagraph-world-map
Comments
If you want a good compromise projection (usually trading area distortion for shape distortion), you're probably going to end up with an interrupted projection of one form or another (the interrupted Goode Homolosine projection is popular).