🚀 go-pugleaf

I once built an eight tier chess, er, "cube"
with planes of plexiglass.  It looked cool
as hell, but playability sucked.  Moving a piece
onto a different plane was really too complicated
for me and my sibs; the vectors for diagonally
moving pieces were always something we squabbled
over and knight movement was a big headache.

However, your post clicked something in my 
head that I had thought about but put away as
too complicated: a three person chess game.
As I had two sibs, we always tried to figure
out ways we could all play against each other
at the same time - must've cut apart and taped
together a half dozen chessboards but nothing
compelling ever came of them.  

How about this: take a chessboard, place another
chessboard at a right angle to it, then place a
third chessboard orthogonal to the other two.  In
other words, like the way they connected the planes
in "Contact" to figure out the code.  One plane or
board for each player, with pieces arranged
traditionally.  Pieces would move as they would
on a two-dimensional surface, but their playing
surface would actually be bent by a third dimension.

Let me know if this seems apropos.  It's interesting
enough that I might work on it myself!