I wonder if there has been any success in popularizing alternate connectivity. I am think something like triangles where each intersection would have like six liberties, or hexagons where each intersections would have three liberties, other tessellations. I am sure it has been done before.

I had some fun with a trihexagonal tiling:

viewtopic.php?f=45&t=5463

This one's interesting because it's still 4 liberties per stone, but it has very different dynamics. I don't know how hard it would be to play, I've really only looked at it by myself.