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While starting out on writing the Raumherichess page I realised a way of
generating any number of 3d variants. It is notable that the hex diagonal
is problematic for its pieces' ease in slipping through between other
pieces. This is the reason why Siegmund Wellisch so underused it, and why
the geometry has triggered pure-orthogonal games like Toccata. Well, what
about the standard, square-board diagonal? With hex boards that means going
3d, but it surpringly easy to set rules that apply widely. Have 5 levels.
The top and bottom levels are the original 2d game, but with the
royally-restricted piece made capturable. The next levels in replace
orthogonal pieces with standard-diagonal pieces - Rooks with Bishops,
Wazirs with Ferzes, Cannons with Arrows, et cetera - and hex-diagonal with
hybrid-diagonal. If there are any oblique pieces Sennight goes to
Heffalump, Aurochs to Fortnight, Student to Calibrator, Overscore to Tutor,
et cetera. The middle level then substitutes the compounds of both, with
any royal restriction restored. Here are some examples extrapolating the
91-cell 2d board to a 455-cell 3d one.
	Example 1: Wellisch. Each outer level has a Wazir, a Vicereine, 2 Rooks, 3
Viceroys, and 8 Points aside. The last 2 piece types are bound to those
levels, but the rest can move straight up or down as well. Each even level
has a Ferz, a Druid, 2 Bishops, 3 Rumbabas, and 8 Crosses aside. The middle
level has a King, a Worldqueen, 2 Queens, 3 Bellmen, and 8 Princelings
aside.
	Example 2: Glinsky. Each outer level has a Duke, a Duchess, 2 Rooks, 2
Sennights, 3 Unicorns, and 9 Migrants aside. The last 3 piece types are
bound to their starting levels, but the rest can move straight up or down
as well. Each even level has a Landlord, a Pontiff, 2 Bishops, 2
Heffalumps, 3 Dicorns, and 9 Migrant Crosses aside. The middle level has a
Worldruler, a Worldrider, 2 Queens, 2 Sennight+Heffalump compounds (I'm
going to have to name those, aren't I?), 3 Tricorns, and 9 Migrant
Princelings aside.
	Example 3: McCooey. Only the forward-only pieces differ from example 2 - 7
Brokers aside on each outer level, 7 Wielders aside on each even level, and
7 Brokerwielders (alias Breakerwarders) on the middle level.
	Example 4: Rose Chess. Only the forward-only pieces differ from example 2
- 6 Lowlanders aside on each outer level, 6 Octchicks aside on each even
level, and 8 Lowocts (alias Highhexes) on the middle level.
	Example 5: AltOrth. Each outer level has a Wazir, a Rook, 2 Forerooks, 2
Hindrooks, 3 Viceroys, and 7 Migrants aside. The last 2 piece types are
bound to those levels, but the rest can go straight up or down as well.
Each even level has a Ferz, a Bishop, 2 Forebishops, 2 Hindbishops, 3
Rumbabas, and 7 Migrant Crosses aside. The middle level has a King, a
Queen, 2 Forequeens, 2 Hindqueens, 3 Bellmen, and 7 Migrant Princelings
aside.
	Example 6: Liu Yang. Each outer level has a Duke, 2 Rooks, 2 Cannons, 2
Unicorns, 2 Slings, 2 Sennights, and 9 Brokers aside. The last 4 piece
types are bound to those levels, but the rest can go straight up or down as
well. Each even level has a Landlord, 2 Bishops, 2 Arrows, 2 Dicorns, 2
Swords, 2 Heffaluimps, and 9 Wielders aside. The middle level has a
Worldruler, 2 Queens, 2 Tanks, 2 Unicornlines, 2 Slinglines, 2
Sennight+Heffalump compounds, and 9 Brokerwielders aside.
	Example 7: Hex Shogi 91. Each outer level has a Duke, a Rook, a Unicorn, 2
Superbrasses, 2 Azures, 2 Wings, 2 Supersenhelms, and 9 Points aside. Of
these only Dukes, Rooks, and Superbrasses can change level, straight up and
down. Each even level has a Landlord, a Bishop, a Dicorn, 2 Superpearls, 2
Rubies, 2 Mitres, 2 Superrumtusks, and 9 Crosses aside. The middle level
has a Worldruler, a Queen, a Tricorn, 2 Superworldprinces, 2 Worldbellmen,
2 Princesses, 2 Super[Senhelm+Rumtusk]s, and 9 Princelings aside.
	An alternative in all the above is to replace all the forward-only pieces
with Pawns. Their move in this geometry is forward to an adjoining column,
on the same level to an empty cell but changing level when capturing. In
the Wellisch and Shogi cases each Pawn has a choice of two vertical planes
to move in, but in the rest Pawns operate in separate groups of five each
on a separate 5-file plane.