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Man and Beast 01: Constitutional Characters

This is the first in a series of articles about pieces in Chess variants. It covers the long-range piece types in FIDE Chess and corresponding pieces in 3d and/or hex FIDE analogues. It is specific to radial pieces, which pass through the centre of a cell or only its borders. Three types of radial direction are covered here. Orthogonal directions, so called because they pass through cell boundaries at right angles, have the shortest steps, whose length as defined as 1. Standard diagonal (SD) directions, the diagonal of the standard square-cell geometry formed by simulatneously moving equal numbers of orthogonwsal steps at right angles have steps of length root-2. Nonstandard diagonal (ND) directions include the diagonals outside a 2d plane in the cubic geometry, colloquially called triagonal, and the diagonals of the 2d hex board. I use the same term for both as both have steps of length root-3 and both can be expressed as equal numbers of steps in an orthogonal and a standard-diagonal direction at right angles, the first on the cubic board and the second on the xyrixa geometry, as featured in Mark Thompson's Tetrahedral Chess.

The acknowledgments, overview, and glossary to the series can be found here. Established pieces have a link to their Piececlopedia page. The images used in this series, and indeed in most of my pages, can be found here.

Pieces

FIDE Chess has two simple radial pieces: the orthogonal ROOK, originally a chariot that in peacetime might transport a household and now represented as a tower of a stately home; and the standard-diagonal BISHOP, named after the rank of clergy which, in the Anglican church, has seats in Britain's House of Lords - for the time being. Shogi also has these pieces under names appropriately meaning Flying Chariot and Angle Mover. The corresponding nonstandard-diagonal piece is termed a UNICORN in the best-known cubic game, Raumschach, and as a supporter of Britain's royal arms the fabulous creature so named continues the lordly theme. I have also seen it called Mace (for brevity, in Ray Bornert's game), Fool, Elephant (foreign names for Bishop, in Ervand Kogbetliantz' game and Michael Ward's Octahedral Chess - although pieces leaping or stepping exactly two squares are also called Elephants) - or on 2d boards made of hexagons (which have a nonstandard diagonal but no standard one) by the name Bishop itself! This last is ill-advised as the Unicorn in this form can coexist with the Bishop on 3d hex boards. All three have obvious images. These are the Rook and Bishop moves in a square plane and the Rook and Unicorn moves in a hex plane:


The above pieces are long-range. Also well-established, though not in FIDE Chess, are one-step versions of the Rook and Bishop, whose names WAZIR and FERZ mean royal advisers. These move only one cell in their directions. The short-range form of the Unicorn I term VICEROY for reasons that will become apparent. Another one-step piece of note is Xiang Qi's GENERAL, identical to the Wazir except that it is subject to the royal restriction that its imminent capture loses its player the game. In Xiang Qi and many of its variants both General and Ferz are restricted to not leaving a FORTRESS (also called a Palace or Ninecastle) comprising the intersection of the back three ranks and middle three files. The Ferz in other regional and historic games, however, and the General in non-XQ and especially hex variants, are not so restricted. As hex pieces Siegmund Wellisch and Mark Thompson call the Viceroy a Knight and the General a King; others call the cubic Viceroy a Sprite. However Knight usually means the best-known oblique piece, and Sprite resembles Stripe, which I use for another such piece, both covered in MAB 03: From Ungulates Outward. Courier mixes long- and short-range pieces in the square-cell directions, the Wazir under the name Schleich (sneak or spy), while John Smith's Neptune has the hex Unicorn and Viceroy under the names Minister and Zenbln (a creature from the fictionalised world of the title). The Wazir and Ferz have established images, and there is an image obviously meant to represent a General, but for the Viceroy I deliberately chose one that has a miniature versions, for reasons that will become apparent. These are the Wazir and Ferz and General moves in a square plane and the Wazir and Viceroy and General moves in a hex plane:

On square-cell boards Bishops and Ferzes are colourbound, meaning that they can reach only alternate squares - each player's right-hand Bishop those of the paler colour and their left-hand one those of the darker colour in the FIDE case. On hex boards Unicorns and Viceroys are bound to one cell in three. On 3d boards the bindings vary as shown in the following table. Rooks and Wazirs are unbound in all geometries. Cubic is the commonest 3d board, xyrixa that used in Tetrahedral Chess, and hex-prism a 3d stack of hex boards pioneered in my own Honeycomb Chess.

cubic xyrixa hex-prism
Square planes through each cell 3 @ right angles 3 @ right angles 3, none @ right angles
Hex planes through each cell none 4, none @ right angles one
Orthogonals through each cell 3 @ right angles 6 in 3 mutually perpendicular pairs 3 (hex) in the hex plane, 1 (interhex) @ right angles to it
Planes through each orthogonal 2 square @ right angles 1 square, 2 hex hex and one square @ right angles (hex), all 3 square (interhex)
SDs through each cell 6 in 3 mutually perpendicular pairs 3 @ right angles 6 in 3 mutually perpendicular pairs
Planes through each SD 1 square 2 square @ right angles 1 square
NDs through each cell 4, none @ right angles 3 in the hex plane 12, none @ right angles
Planes through each ND none 1 hex hex only
Bishop/Ferz binding 1 in 2 1 in 2 of alternate square planes, making 1 in 4 unbound
Unicorn/Viceroy binding 1 in 4 unbound 1 in 3 of single hex plane
On boards with concavities, moves along both kinds of diagonal may be further restricted by the ONE FOOT IN THE GRAVE rule, under which each step of the move can be made only if it is between corners of a square, rhombic, or cubic block of cells with no cells missing, as if it would lose its footing trying to pass over the concavity itself.

The Wazir and Ferz are switching on square-cell boards. The Wazir is colourswitching, always moving from one Bishop and Ferz binding to the other, the Ferz rankswitching, always moving from an odd to an even rank or vice versa. This prevents them returning to a cell in an odd number of moves. The Wazir retains this property on cubic boards, as there remain 2 Bishop bindings, but not on boards with a hex element, where it can triangulate - return in 3 moves, the minimum odd number - on an equilateral triangle of orthogonally adjacent cells. Conversely the Ferz retains it on xyrixa and hex-prism boards, as it always moves from an odd to an even hex board or vice versa, but not on cubic ones, where it can triangulate on an equilateral triangle of diagonally adjacent cells. The Viceroy on a cubic board switches between odd and even ranks and indeed levels, but on a pure hex board all symmetric pieces - ones able to move in every direction of a particular kind - can triangulate. This page's long-range pieces are never switching.

Shogi has forward-only (FO) versions of Rook and of Wazir, and larger Shogi variants FO versions of Bishop and of Ferz. These too can be extrapolated to the ND. As their Japanese names translate respectively as the cumbersome - and unrelated - Fragrant Chariot, Foot Soldier, Ramshead Soldier, and Stone General the best approach for English names is to start from scratch. Long-range pieces I name after attributes of the symmetric piece - WING, MITRE, and HORN - and short-range ones after the shape of their cubic moves as viewed from in front - POINT, CROSS and SALTIRE. As well as an attribute of both stately homes and biological rooks, Wing indicates the piece's place on the Shogi board in sporting terms, echoing the use of "Swing Low, Sweet Chariot" as a sporting anthem. Bindings and switchings are rarely relevant to FO pieces, which have access to an ever-dwindling range of cells until (as is usually possible) they are promoted. My variant Partnership Mitregi features an alternative to promotion: each army is moved by a team of two players who have opposite forward directions. On hex boards forward is taken to mean just the most forward directions. Forward orthogonal/SD/ND directions number 1/2/0 on a face-to face and 2/1/0 on a corner square-cell board, 1/0/2 on a Glinski and 2/0/1 on a Wellisch hex board, 1/4/4 on a face-to face and 2/5/2 on a corner-column cubic board, 1/2/2 on a Glinski-level and 2/4/1 on a Wellisch-level hex-prism board, and 1/6/0 on a hex-ranked hex-prism board. Hex-ranked boards can therefore not have Horns or Saltires. There are at least 5 orientations for a xyrixa board. Forward directions on these number 1/2/4 if face-to-face square-level, 4/1/4 on Mr. Thompson's own orientation which can be considered corner square-level or square-ranked, 3/3/3 on hex-ranked ones. Hex-level xyrixa boards are complicated by asymmetries. For all these pieces I use miniature versions of the images for the symmetric pieces, save the Horn as there is no miniature Unicorn image. Here are the Wing, Mitre, Point, and Cross moves on a square-cell board, first face-to-face and then corner; and the Wing, Horn, Point, and Saltire moves on a hex board, first Wellisch and then Glinsky/McCooey:






There are also Pentagonal 2d geometries, whose cells are pentagons. Two of these are used on these pages, one in Daniil Frolov's Pentagonal Chess and another in SerPent Chess. A third may be derived by rotating Mr. Frolov's board by 90°. From a pentagon the Wazir can move to 5 adjoining cells and a Ferz, in the strictest sense, to only 2. The limits bind a Ferz very severely - to a rank diagonal, a chain of successive cells alternating between two ranks on the Frolov board or the orange and blue cells in the SerPent board "sideways" directions, or a file diagonal, a chain alternating between two files on the rotated Frolov or red and green cells in its "forward" or "backward" ones. Only by being able to return from capture, or by a King Swap in the Yang Qi style, can a single Ferz make all possible moves. The Point has two directions from a cell with (from its player's viewpoint) a rear edge, and one from other cells, except on the rotated Frolov board where they always have just the one. On a SerPent board the Cross is specific to file diagonals with a single direction. On the rotated Frolov board it again has just the one. These geometries have no long-range Straight pieces, as neither the orthogonals nor the diagonals line up opposite each other. No virtual movement diagrams are available for these geometries.

Stacking up boards of either kind in a 3d board with a Straight orthogonal at right angles to them makes things more promising. Though not affecting the Point this adds 2 interlevel directions to a Wazir and 10 - above and below the same-level Wazir ones - to the Ferz, of which the Cross also gains 2 or 4 depending on position. This gives the Cross 4 directions from any Frolov-level cell, 3 from a cell on a SerPent-level file diagonal or any rotated-Frolov-level cell, and twice as many as a Point from a cell on a SerPent-level rank diagonal. It also adds a Rook moving any distance up or down but still only as a Wazir on the level, a severely bound Viceroy with four directions above and below the same-level Ferz ones, and a Saltire specific to file diagonals with the two forward Viceroy moves. The Bishop, Unicorn, Wing, Mitre, and Horn remain unavailable.

Triangular-cell boards can be considered as hex boards with pieces unable to stop on cells of a particular colour. This restriction does not affect the Unicorn or Viceroy. This can be generalised to pieces unable to to stop on any specified group of cells, defaulting to a Unicorn binding on a hex cell and, I would suggest, a Dabbaba binding on a rectilinear one. These could be the whole army or mixed with unrestricted pieces. AVERSE pieces avoid the same group of cells regardless of army, typically on a board with a cell at the centre. This is the setup rendering hexagonal cells triangular. CAMOUFLAGE-AVERSE pieces avoid a different group for each army, typically on a board with a vertex at the centre. This term is because when applying to entire armies the avoided cells can be given the same colour as the pieces. This setup renders a hex board as a different triangular-cell one for each player. On hex boards the AVERSE WAZIR regains its colourswitching. The Glinski orientation does not allow an AVERSE POINT, which in the Wellisch orientation makes alternate moves along the two directions. This is also true on a hex-prism board, where the AVERSE BISHOP and AVERSE FERZ regain binding to half the board - one remaining colour on odd, and the other on even, hex planes. Likewise Glinski-level boards have no AVERSE CROSS. Hex ND pieces are unaffected. As I have not developed variants using such pieces I use no images for them.

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Further pieces combine corresponding moves in two or more types of direction. The FIDE KING and QUEEN are General+Ferz and Rook+Bishop; the latter fittingly blends the domestic and advisorial. These are of course the major Chess-themed characters in the second (and card-themed in the first) of Lewis Carroll's Alice books. The Queen is occasionally given other names - Guard as a Poison Chess promotee, Favourite or Rookbishop in some 3d games using Queen in another sense. Wazir+Ferz gives a capturable version of the King which I prefer calling a PRINCE, although it is also called Commoner, Guard, or Mann (King's Henchman). This piece can triangulate even between square cells, not by the equilateral means of the hex simple piece, but by an isoceles right triangle of 2 orthogonals and a diagonal. For FO compounds I lower the rank to term Wing+Mitre PRINCESS, Point+Cross PRINCELING. The Glinski-ranked hex-prism board does not suit AVERSE PRINCELINGS. The three symmetric pieces have established images abd again I use them miniaturised for the FO ones. Here are the King, Queen, and Prince moves; the Princess and Princeling moves face-to-face, and the same on corner orientation.

In FIDE Chess, an unmoved King and Rook with no intervening piece can make a special move together called CASTLING. The Rook moves to just short of the King's cell, but the King simultaneously moves two steps in the opposite direction. No part of the King's move may be threatened by an enemy piece. As the King's move is a special two-step one that cannot be done without also moving the Rook, but the Rook's move without the King's is valid, it is usual to move the King first and then the Rook behind it. Many variants inherit this rule, someties in an enlarged form, and some large variants relax the rule to say that both King and Rook must not have left a supersquare of 2x2 cells. Some variants, especially 8x8x8 3d ones, have a diagonal version of Castling which I term CATHEDRALLING, with the same restrictions.

Combining orthogonal and diagonal pieces I preserve patterns of male and female names and relation of social rank, listed here in the King Queen Prince Princess Princeling order. Some inventors extend FIDE names to pieces with nonstandard diagonal moves, but I prefer consistency between the same pieces on square, hex, and 3d boards. With nonstandard diagonal: GRANDDUKE (ruling duke in e.g. Luxembourg) DUCHESS DUKE COUNTESS COUNT (or exact synonym Earl). The first Alice book features a duchess. With both kinds of diagonal: EMPEROR (hence Viceroy for Emperor "minus" King) EMPRESS ARCHDUKE (title for sons of certain emperors) CONQUERESS CONQUEROR. For combinations only of diagonals I assume all to be capturable and dispense with the male-female divide: GOVERNOR (British sovereign's title in Anglicanism) BARON MISSIONARY (promoteer of an empire's established religion) HEIR. Movement digrams are composites of those already shown, and cannot be shown in full in a single plane for the imperial and baronial groups, but it i sworth showing the piece images that I use throughout my variants. As there are no images combining Unicorn or Viceroy images with others I mark Viceroy compounds with a single fimbriation giving a "3d" look and Unicorn compounds a double one. Here are a column each of pieces in the orthogonal, SD, ND, royal, ducal, imperial, and baronial groups, where I have images for them:

Long- and short-range moves can be mixed. Shogi's Rook and Bishop can gain each other's shortest moves, but the promotees' Japanese names are again hard to extrapolate so again I start from scratch. Rook and Wing moves attract female names, usually the feminine of the version without that move, and Bishop and Mitre moves without them attract religious names. Rooks are enhanced by Ferz to CHATELAINE (lady of a stately home), Viceroy to VICEREINE, and Baron to BARONESS; likewise Wings by Cross to CARYATID (column in the shape of a woman), Saltire to VIRAGO (generic aggressive woman sharing first two letters of Vicereine) and Heir to HEIRESS. Bishops are enhanced by Wazir to PRIMATE (otherwise unused synonym for archbishop), Viceroy to MODERATOR (leading figure in some bishopless churches), and Duke to POPE; likewise Mitres by Point to ABBOT (has plainer mitre than bishop), Saltire to ELDER (subordinate to moderator), and Count to NUNCIO (papal diplomat). The last verse of Lewis Carroll's Gardener's Song refers to an "argument that proved [the gardener] was the Pope". Unicorns are enhanced by Wazir to BESIEGER, Ferz to HERETIC, and Prince to USURPER (characters attacking castles, churches, and royalty); likewise Horns by Point to RAM, Cross to DEBATE (devices used by their symmetric counterparts), and Princeling to PRETENDER. Enhanced does not necessarily mean promoted. Such pieces may occur through promotion of the long-range component, as in Shogi and Tunnelshogi, but may also be array pieces as in Mongolian, Wellisch hex, and Duke of Rutland's Chess. My variant Avon features an alternative to promoting Caryatids and Abbots: each army is moved by a team of two players who have opposite forward directions. Here are the movement diagrams for the established Chatelaine and Primate images; augmented miniature images of the Caryatid and Abbot, first face-to-face and then corner; and the hex forms of Vicereine, Virago, Besieger, and Ram:



Short-range moves can also be added to long-range pieces that are already compound. Queen+Viceroy is DIARCH (joint ruler, such as Britain's William and Mary), Duchess+Ferz DOWAGER (lord's widow and his successor's mother), and Governor+Wazir REGENT (prince ruling on incapacitated king's behalf). FO equivalents are Princess+Saltire=PRESUMPTIVE (qualifier for heiress to king who doesn't have sons but might yet), Countess+Cross=DEVOTEE (the widowed often grow more devout), and Missionary+Point=COMMISSIONER (pun on common letters of mission, which is presumably commissioned!). Here are the piece images for the Baroness, Moderator, Pope, Heretic, Usurper, Diarch, Dowager, and Regent:

Pieces with a Rook or Wazir move, or on one of the hex 3d geometries, are clearly unbound. Less obviously those combining a Bishop or Ferz move with a Unicorn or Viceroy one on a cubic board are also unbound as the bindings are independent. This means that the Unicorn and Viceroy can reach 1 in 4 cells of both Bishop bindings rather than alternate cells of one, and the Bishop and Ferz alternate cells of all 4 Unicorn ones. On cubic boards the King/Prince and Baron are freed of their components' switchings but the Grandduke/Duke is not as it still alternates between Bishop bindings. On boards with a hex element none of these compounds are switching. The Count/-ess, Missionary, Heir/-ess, Conquer-or/-ess, Virago, Elder, Nuncio, Ram, Debate, Pretender, Presumptive, Devotee, and Commissioner can exist only on boards where their Horn or Saltire component can.

The King and Prince have 7 directions from a pentagon, and 19 from a pentagonal prism. The latter also adds a Grandduke and Duke with 11 directions, a Baron with 16, and an Emperor and Archduke with 23. They also add a Chatelaine, Vicereine, and Baroness that are long-range only at right angles to the Pentagonal-board levels. The Princeling, Count, Heir, and Conqueror also have the sums of their components' directions. These are all the compound pieces of this page available on a Pentagonal or Pentagonal-prism board.

Notes

Divergent radial pieces, such as the FIDE Pawn, have their own article, MAB 02: Shield Bearers.

Symmetric and FO moves can also be mixed. Shogi has such pieces, whose Japanese names can be extrapolated. It was mixed-range forms of these that put me off naming FO pieces after symmetric ones prefixed by either Shorn (to rhyme with Pawn, at least in Eastern English accents) or Lance (as in Corporal). There are so many extrapolations that they too have their own article, MAB 04: Generalised Generals.

Straight non-coprime radial pieces are covered in my later articles MAB 06: The Heavy Brigade, and Curved and Crooked forms of this page's pieces in MAB 09: Mighty Like a Rose.

Straight coprime pieces using a fourth kind of radial direction specific to hex-prism boards have their own article, MAB 10: The Hybrid Diagonal. This is to keep this page simple for readers less interested in hex-prism geometry.

Pope is also the name of a piece in Fergus Duniho's 2d variant Fusion Chess, moving like a Primate but royally restricted. It is deliberate that my usage is for a piece distinguishable from the Primate only by moves beyond a single rectilinear plane.

As the Baron can triangulate on a cubic board (because its Ferz component can), and the Duke cannot, have I named them the wrong way round? I would argue not. For one thing, on a 2d hex board the Duke can triangulate (as all symmetric pieces existing in that geometry can) but the Baron cannot even exist. For another it seems more sense to make Baron the piece whose feminisation is not its long-distance extension as baroness usually means a peeress in her own right whereas duchess - like queen in a context where there is also a king - means a consort. Viceroy is a title whose remit extends only within a specific imperial possession, and may be given to someone of relatively modest rank back home. This makes it a name better fitting a weak piece than it might appear.

While I describe the Bishop in terms of Anglican diocesan bishops in Britain's House of Lords, it is not restricted to representing these. It can represent suffragan bishops as well as diocesan ones (as in Great Stour) or even vary by denomination (as in my Armies of Faith series). In Magna Carta Chess they (and their Knight compound, a Cardinal) represent a Catholic church at a time when it was England's established one.

My assertion that translating mixed-range pieces' Japanese names is too difficult to extrapolate is from experience of trying. Dragonking for Rook+Ferz could be extrapolated to Dragonduke for Rook+Viceroy and Dragonemperor for Rook+Baron, but what of the rest? What has Dragonhorse for Bishop+Wazir to do with any other horsy piece? The Mao, whose move's two stages are in the relevant directions? If so, there are no special terms for stepping versions of the Sexton and Ninja. The Unicorn, by absence, making Unicorn+Wazir Dragonpriest by the Bishop's absence? If the latter, what is to say which of Bishop+Viceroy and Unicorn+Ferz should be Dragonbaron and which Dragoncastle? What about Bishop+Duke, Unicorn+Prince, Queen+Viceroy? What about pieces with a hybrid-diagonal element? What about all the FO pieces? Should Wing+Cross be Dragonprince? Eventually I judged it far better to start from scratch with real titles in keeping with those for purely long- or short-range pieces.

The piece currently named Debate was originally named Xorn after an obscure monster, but I decided that Debate would give a better initial for extrapolations.

This 'user submitted' page is a collaboration between the posting user and the Chess Variant Pages. Registered contributors to the Chess Variant Pages have the ability to post their own works, subject to review and editing by the Chess Variant Pages Editorial Staff.

By Charles Gilman.

Last revised by Ben Reiniger.


Web page created: 2007-10-30. Web page last updated: 2023-09-25

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