I'm in a hotel for one night for work and packed a few solo games. I haven't played TM:AE in a while so I decided to play it first. Wow, I forgot how brutal it can be. I was nowhere near completely terraforming Mars before the rounds ended.
... The valid positions are either all even coordinates or all odd coordinates.
So, your graph paper has a scale of 2 for each line. You can either be on an intersection (all even coordinates) or on a square center (all odd coordinates).
Either way, movement is intuitive. Either move 2 in an orthogonal direction, or (1,1,1) in a diagonal direction.
I'd say this all compares favorably with the better known rhombic dodecahedron tiling.
I'm working on a lot of stuff right now, including, but not limited to:
Full gameplay explanation of Wayfarers video
Two vids on Flamecraft, one guest starring my youngest daughter
Fox Experiment video and write up
But if you'd like to check out my latest video, click the link below and take 4 minutes out of your day to learn about Wayfarers of the South Tigris from #GarphillGames