Playing with a friend we talked of variations that could exist like a 3 dimensional version. Below are our experiments.
Digital versions exist but we set about making real "boards". A problem exists relating to accessing the inner points. The players need a way to get to the center points. One solution is to make the board large enough that you can fit your arm and hand in between the vertices. Doing this there is a limit to the total number of vertices that can exist; if there are too many you can't access the inner vertices. Her work in progress efforts are below, the outer vertices are constructed with string in a wooden frame.
An alternate solution to the problem of accessing the inner vertices is to make a "board" that comes apart into multiple pieces. The photo below are my efforts to make more of a tabletop sized board. It is unfinished but this would be the right hand side. The cube will have a split in the middle so you can move them apart. Distance between vertices was determined by finger size. It still may be a bit tricky to get to some of the inner most pieces.
It is made out of wire soldered together, with some loops for the feet.
The traditional 2D board is 19 by 19 grid. I do wonder about the significance of 19 being an odd number. My wire board is 10 by 10 by 10 and perhaps this even number will have an affect on game play. In future it would be possible to cut it up and make a 9 by 9 by 9 grid if an odd number has significance.
Another problem is what do you use for pieces? We had a few ideas: little loops of pipe cleaners or perhaps a cd / donut shaped discs with a slice in it to slide into place, or perhaps something magnetic. To be explored!