nice idea, but it does not seem very realistic and here is why:
so it is like every player is going against 4, wait if you include the triangles it is every one going against 4 however those on the triangles will have a huge difference from those on squares, and if not used some players will go against 2 others while some have to go against 4 so it is unfair
plus I think you might be overcomplicating it just for the sake of overcomplicating it since you are basically trying to recreate a variation of those multiplayer chess that goes from both sides until reforming a loop, however in here it is worse to play since if it is programmed as a whole Rhombicuboctahedron it will be hard to know how to move away from your square the piees, and if added as a plane where as 4 player chess but 1 in middle and 4 against middle that is different for each person, it is pretty hard to figure plus to play, as well as other players pieces will seem to move disappearing from 1 board appearing on another (it is how electrons seem to work but trust me it is hard as hell to study them, you literally have to be einstein to do so ) and that would also affect you in a way since a piece that jumps from 1 place to another will have a whole new 3 board in range of attack or even more making the possibilities of where pieces might get moved close to infinite wich you might immagine is bad as a player since you litteraly do not know where an attack will come from
thanks for trying to come up with new variants and i liked your gigantic chess, however for this one i really think you should reconsider a whole new way how that might work, or just drop it, since it seems it is pretty hard to actually get from it something that might work (i tried to come up with a way to maybe get it better and i failed)
so basically it is not too realistic as well as not easy to figure out how to play
So this is a Rhombicuboctahedron:
I'm imagining something like 64 smaller square tiles within the "square face" and the triangle faces are unused (to keep things simple - but of course you can add triangle tiles within if you wanted to).
Each army (up to 18 players, suggested for equal proportional distance to other players: 2, 3, 4, 6, 8, 12), inhabits one of the shapes square faces in a formation suitable for the amount of players playing.
I haven't thought of how the armies should be positioned or how things like pawn promotion would work but this is the basis of the idea and you can make variations out of it as well.
Mostly I was trying to go for something that would look like Chess on a Globe but without the annoying super thin tiles up at the North and South Poles. I came up with this. Feel free to come up with set up suggestions. Here's one I'll make that an army could have on one face: