Just as a guess, I'm assuming they can move onto the empty 'side'
squares as per normal movements. The pawns would probably never see the
side squares, barring captures, so there may be a special rule for them.
If a pawn *did* capture to another face, it might very well continue
'forward' until it wraps around, resulting in movement that is 90
degrees from 'normal'. I'm assuming that's what the colored heads are
for; to determing the correct direction of a given pawn, since it might
otherwise result in some complicated bookkeeping.
As far as the corner squares go, I'm going to assume again that you just
can't move 'diagonally' from a corner square onto another face. This
would make things interesting for bishops, and pawns would have even less
opportunity for capture, but it would also make for some interesting
'shadows' of the board, places for kings to both hide and be trapped in,
that sort of thing.
In any case, like I said, I'm assuming. Rule Zero and all that. I know
I'd seriously consider purchasing one if the cost could be kept
reasonable. I WOULD like to see the rules, though.