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Another one mad idea. I see that it have a few defects, and it may contain
other defects i didn't notice, and therefore i created subject to discuss
it. Also, i'm afraid, this game may be unplayable at all, and it's just a
funny time-waste.
Inspiration if from Charles Gilman's 3D Switchback Xiang Qi.

Consider 3x3x3x3 board.

    3--- --- ---
III 2--- --- ---
    1--- --- ---

    3--- --- ---
 II 2--- --- ---
    1--- --- ---

    3--- --- ---
  I 2--- --- ---
    1--- --- ---
     abc abc abc
      A   B   C

Lowercase letters to mark files, Arabic numerals for ranks, upercase letters
for 'hyperfiles', Roman numerals for 'hyperranks'.

To set pieces, look at this scheme as at 2-dimensional board and set pieces
as in usual Shogi (and promotion zones are same), but rook must face rook,
not bishop. If rook will face bishop, it will be able to capture it on
first turn, and in this game rook  is weaker. However, rook still can
capture another rook (protected, of course), and other pieces can contact
with opponent on very first turns, and it's the main defect that scares
me.

If you are familar with other 4D chess varinats, you probably already
understood the way of movement of regular pieces. Here moves of piece 'x'
are marked with 'o' if orthogonal and 'd' if diagonal:

--- -d- ---
-d- dod -d-
--- -d- ---

-d- dod -d-
dod oxo dod
-d- dod -d-

--- -d- ---
-d- dod -d-
--- -d- ---

There are no triagonal and quadrogonal moves.
Question 'What are orthogonally-forward moves here?' is simple (there are
two directions, and pawn can't be dropped if same rank AND hyperrank that
contains another pawn, or simply rank, if you are watching board as
2-dimensional). Same question about diagonally-forward moves is more
complicated. Consider diagonal step as two orthogonal steps. One possible
solution is that these orthogonal steps must'nt be both sideways and
neither may be 'backward-directed':

--- -d- ---
-d- dod -d-
--- --- ---

-d- dod -d-
--- -x- ---
--- --- ---

--- --- ---
--- --- ---
--- --- ---

Another solution is that at least one of these orthogonal steps must be
'forward-directed', it gives two more possible moves:

--- -d- ---
-d- dod -d-
--- -d- ---

-d- dod -d-
--- -x- ---
--- --- ---

--- -d- ---
--- --- ---
--- --- ---

In either case, silver general have more moves than gold general, and thus
there is no point of promoting silver to gold. Perhaps, thier places in
promotion hierarchy should be be swapped, and pawns, lances and horses
should promote to silver as well.

Horse's leaps are any two steps forward+any one step sideways:

--- --- ---
--- --- ---
-h- h-h -h-

--- --- ---
--- --- ---
--- --- ---

-h- h-h -h-
--- --- ---
--- -x- ---

Note that there are not only cells, where it can't move, but also cells,
where it will be able to make only one leap further. And these are the
whole second hyperrank.

Another serious problem is too mobile king. Perhaps, it should be able to
move only orthogonally. Or, maybe, replacing kings with two Shogi emperors,
that are able to leap to any cells (but in practice, only to cells,
protected by friendly pieces) will also help?

Another, probably, the most efficient way out is to play it as 'Walkers
and Jumpers': some pieces treats board as 2-dimensional. In this case,
kings, rooks and bishops (thus, no need for mirror symmetry). Probably,
pawns, knights and lances are best as being both 'Walkers' and
'Jumpers'.