Gutenschach

For the most part I use the same names as Mr. Smith for those pieces that he invented. Base, however, has a problem in that it is the heraldic term for the lower part of a shield. For that reason I have used it as a suffix along with chief (the upper part), dexter (the right, from the viewpoint of the man holding the shield), and sinister (the left, likewise) in my piece article Man and Beast 12: Alternative Fronts. That article added: "If a variant rotates only one piece, they can be abbreviated to just Dexter, Sinister, ... Chief, and Base." As this refers to rotated pieces which are essentially weak, it seemed logical to give a very strong piece a very different name. Eventually I settled on Foundation, which has the double meaning of:
1 the subterranean structure that keeps a building stable; and
2 an institution such as a college or hospital.

Setup

    a   b   c   d   e   f   g   h
   --- --- --- --- --- --- --- ---
s |Hos|Stu|Tac|Tac|Eng|Eng|Stu|Rou|
   --- === === === === === === ---
t |Lab#Sci|Rep|Rep|Tec|Tec|Net#Rev|
   --- --- === === === === --- ---
u |Tac#Rep#Pla|Apo|Apo|Phy#Tec#Eng|
   --- --- --- === === --- --- ---
v |Tac#Rep#Sur#Uni|Lib#Exp#Tec#Eng|
   --- --- --- --- --- --- --- ---
w |Att#The#Sur#Pre|Spy#Exp#Fou#Hea|
   --- --- --- === === --- --- ---
x |Att#The#Phy|Str|Str|Pla#Fou#Hea|
   --- --- === === === === --- ---
y |Lab#Net|The|The|Fou|Fou|Sci#Rev|
   --- === === === === === === ---
z |Con|Pri|Att|Att|Hea|Hea|Pri|Amb|
   --- --- --- --- --- --- --- ---

Pieces

Four simple piece types alternate between directions of the same kind:
The FOUNDATION (called the Base in Prince, see introduction) is based on the Girlscout, making 90° turns between two Rook directions. It inherits the unbound character of Rook and Girlscout, and is a distinct piece in 2d as well as 3d. It moves between opposite corners of any otherwise empty rectangle, with orthogonals as sides, of cells within a rectilinear plane, including as a Rook.
The THEORIST is based on the Boyscout, making 90° turns between two Bishop directions. It inherits the binding of Bishop and Boyscout, and is a distinct piece in 2d as well as 3d. It moves between opposite corners of a rectangle, with standard diagonals (the Bishop directions, SD for short) as sides and all other cells of its binding empty, of cells within a rectilinear plane, including as a Bishop.
The TECHNICIAN is based on the Longboyhexer, making 60° (note the different angle) turns between two Bishop directions. It inherits the binding of Bishop and Lbh, and is indistinguishable from a Bishop in 2d. It moves between the furthest corners of an otherwise empty 60-120 parallelogram, with SDs as sides, of cells within a plane forming a hex array of cells of its binding, including as a Bishop.
The REPORTER is based on the Longrangescout, making 70° turns between two Unicorn directions. It inherits the binding of Unicorn and Lrs, and cannot exist in 2d. It moves between the furthest corners of a 70-110 parallelogram, with nonstandard diagonals (the Unicorn's directions, ND for short) as sides and all other cells of its binding empty, of cells within a plane at 45° to two reclinear ones and 90° to the other, including as a Unicorn.

Four simple piece types alternate between directions of different kinds:
The HEALER is based on the Rhino, making 45° turns between a Rook direction and a Bishop direction. It inherits the unbound character of the Rhino, and is a distinct piece in 2d as well as 3d. It moves between the furthest corners of a 45-135 parallelogram, with orthogonals as two sides and SDs as the other two and all other cells empty, of cells within a plane forming a hex array of cells, including as a Queen.
The ATTENDANT is based on the Tapir, making 90° turns between a Rook direction and a Bishop direction. It inherits the unbound character of the Tapir, and is indistinguishable from a Queen in 2d. It moves between opposite corners of an otherwise empty rectangle, with orthogonals as two sides and SDs as the other two, of cells within a plane at 45° to any rectilinear one, including as a Queen.
The ENGINEER is based on the Blocschach Navvy, making 55° turns between a Rook direction and a Unicorn direction. It inherits the Navvy's unbound character, and is indistinguishable from a Rook in 2d. It moves between the furthest corners of an otherwise empty 55-125 parallelogram, with orthogonals as two sides and NDs as the other two, of cells within a plane at 45° to two reclinear ones and 90° to the other, including as a Duchess.
The TACTICIAN is based on the Blocschach Thug, making 35° turns between a Bishop direction and a Unicorn direction. It inherits the Thug's unbound character, rexcept in 2d where it is indistinguishable from a Bishop. It moves between the furthest corners of an otherwise empty 35-145 parallelogram, with SDs as two sides and NDs as the other two, of cells within a plane at 45° to two reclinear ones and 90° to the other, including as a Governor.

Here is a full alphabetical list of back-rank pieces:

The STOCKBROKER moves one step along any of the 9 forward radials with the restriction that the move must be:
(1) noncapturing if orthogonal;
(2) noncapturing if SD and to a file the same distance in/out;
(3) capturing if SD and to a file further in or out;
(4) capturing if ND, including "cutting a corner" with no change in distance in/out.
Note that this makes its moves number:
(a) 3 noncapturing (orthogonal, 1 horizontal SD, 1 vertical SD) and 6 capturing (1 horizontal SD, 1 vertical SD, 4 ND) from files tb/tg/uc/uf/vd/ve/wd/we/xc/xf/yb/yg;
(b) 3 noncapturing (orthogonal, 2 horizontal SD) and 6 capturing (2 vertical SD, 4 ND) from files tc/td/te/tf/ud/ue/xd/xe/yc/yd/ye/yf;
(c) 3 noncapturing (orthogonal, 2 vertical SD) and 6 capturing (2 horizontcal SD, 4 ND) from files ub/ug/vb/vc/vf/vg/wb/wc/wf/wg/xb/xg;
(d) 3 noncapturing (orthogonal, 2 horizontal SD) and 3 capturing (2 vertical SD, 1 ND) from files sb/sc/sd/se/ef/eg/zb/zc/zd/ze/zf/zg;
(e) 3 noncapturing (orthogonal, 2 vertical SD) and 3 capturing (2 horizontal SD, 1 ND) from files ta/th/ua/uh/va/vh/wa/wh/xa/xh/ya/yh;
(f) 3 noncapturing (orthogonal, 1 horizontal SD, 1 vertical SD) and 1 capturing (ND) from files sa/sh/za/zh.
In other words, corner files apart it has the same ratio of move types as a Pawn on a 2d board, the outermost files corresponding to the 2d board's edge files. This is one parallel resulting from all ND moves being capturing; the other is that the move crossing through the centre line corresponds to a Pawn move between two equally central files on a even-file square-cell board.

Rules

There is no Castling for want of a King or Emperor.

Stockbrokers reaching the far rank must be promoted to either a simple planar piece or a compound of two.

Each player must retain two triple compounds from each group - two out of University/Library/Press/Spy and two out of Hospital/Round/Consultant/Ambassador. The winner is thus the first player to capture three triple compounds of either group from the other player.

Notes

A further connection between the piece names Printer and Prince is that of the Printers Bible, so called because the lament "Princes have persecuted me without cause" was misprinted as "Printers have persecuted me without cause".