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Man and Beast 05: Punning by Numbers
IntroductionThis article extends MAB 03: From Ungulates Outward over a 3d superset of the directions considered there, on cubic-cell boards sized up to 9x9x9 (8Â³). These boards too have coprime oblique leapers with 1 odd coordinate which switch between Bishop bindings, and ones with 2 which share the Bishop's binding, square-board pieces being special cases with one even coordinate being zero. Many 2-odds pieces have names related either to religion or to imparting wisdom. A particular substrand of this, persons taking a vow (Monk, Votary, Avower), ties in with the Arrow for which vow is a metaphorical meaning in Chinese, another piece with the Bishop's binding.
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.
PiecesFor some leapers with 2 odd coordinates the longest coordinate is the sum of the others, allowing a Ferz-like equilateral triangulation on a cubic-cell board. Such a piece is this article's shortest-range one, the 2:1:1 leaper. On reading that problematists term this a SEXTON, a pun on its Square Of Leap Length (SOLL) of 6 as well as a religious name for a piece sharing the Bishop's binding, I hit on the idea of extending the punning theme. It is no accident that this piece has thrice the Ferz' SOLL: its move equates to two Ferz moves with a 60Â° turn in between. For any m+n:m:n leaper - length 2(mÂ²+nÂ²+mn) two of its leaps at that angle form a 2m+n:m+2n:m-n leap, length (4mÂ²+4mn+nÂ²)+(mÂ²+4mn+4nÂ²)+(mÂ²-2mn+nÂ²)=6(mÂ²+nÂ²+mn). If mÂ²+nÂ²+mn is not a multiple of 3, both are coprime, but both are also of even SOLL. Given my method of naming of non-coprime oblique pieces and compounds with radial pieces these pairs cannot share a first consonant and vowel.
A third nonzero coordinate removes the guarantee of pairing through right angles. The next shortest-range piece, the 2:2:1 NINJA (SOLL 9), has a square-style dual of sorts. Two Ninja moves at right angles give either the non-coprime 3:3:0 move of the Tripper of the next page or a 4:1:1 move. The piece with the latter move I therefore term NIMEL and its compound with the Ninja NINTU (a Mesopotamian mother deity, as used in the first page of my Armies of Faith series). My Ecumenical Eurasian Ninjachess uses the trio together.
Another aspect of the Ninja/Nimel SOLL ratio of 2 is that pieces repeating a coordinate have moves comprising orthogonal and diagonal coordinates at right angles, which the xyrixa geometry as featured in Mark Thompson's Tetrahedral Chess also has. Where a piece's third coordinate is odd, m:m:n say, with SOLL 2mÂ²+nÂ², its 2m:n:n semi-dual's SOLL is 4mÂ²+2nÂ². The Sexton is the semi-dual of MAB 01's radial Viceroy, but most pairs are of two oblique pieces. While reserving the -mel suffix for true duals I attempt to give semi-duals a common first consonant and vowel. The pair have moves at right angles to each other, means that the 2m+n:m-n:m-n and 2m-n:m+n:m+n leapers, the pair's hypotenuse pieces (or hypotenuses for short), has thrice the shorter-range one's SOLL. These pieces inherit the odd (or in cases considered in later articles, even) shorter-range piece's SOLL. The Viceroy is the hypotenuse of the Wazir-Ferz pair, and the Ninja and MAB 06 Trebuchet those of the Viceroy-Sexton pair.
Oblique leapers with 3 odd coordinates share the Unicorn's binding and lack duals as any two successive 3-odds moves form a non-coprime 3-even move, necessarily not with twice the SOLL, but may have semi-duals. Likewise pieces such as the Sexton whose SOLL divides by 8 with remainder 6 have no cubic dual, bound or unbound, but may be a 3-odds piece's semi-dual. Such a pair are the 3:1:1 ELF (plural ELVES) and its semi-dual the 3:3:2 LECTURER. Elf puns on the German for its SOLL of 11 as well as linking with both Unicorn as mythical creature (as used together in my Heathen Europe Chess) and Tolkien. Lecturer is more of a stretch but it is not unknown for 22-year-old postgraduates to fund their own studies by lecturing to undergraduates.
Pieces repeating a coordinate have, like 2d oblique leapers, 24 directions on cubic boards. Pieces with three distinct nonzero coordinates have 48. This is analogous to oblique leapers on 2d boards having two distinct nonzero coordinates and so twice the directions of radial ones, with only one. The first such piece, the 3:2:1 FORTNIGHT, can triangulate. Note that this geometry has no piece with SOLL 7 and can in fact have none with a SOLL one less than any multiple of 8. The word Fortnight means a period of two Judaeochristian seven-day weeks, but also hints at a knight defending a fortress. As this fits in with the Ninja and, in Tolkien, Elf being warriors the 3:2:2 leaper is the FENCER, starting with the last two letters of the Giraffe whose SOLL of 17 it shares. I have chosen piece images as far a Fencer, and here they are in increasing SOLL order:
Pieces whose coordinates include both 4 and 3 clearly share the SOLL of the piece combining the same remaining coordinate with 5 and 0. Where the common coordinate is even I reverse the 2d piece's name - 4:3:2 RYTAS, 4:4:3 ROTCER, 6:4:3 NOSRAP, 8:4:3 EMONORGA - where it is odd that of the unbound dual - 4:3:1 ARBEZ, 4:3:3 EFFARIG, 7:4:3 OGNIMALF. Arbezes and Ognimalfs can triangulate, the latter only just on an 8Â³ board by making each move edge-to-edge (e.g. va8, zd1, sh4). The Effarig is the Fencer's semi-dual. The very special case of 5:4:3 I term EPOLETNA. Among leapers coincidentally sharing a 2d one's SOLL I term the 6:4:1 one (53 like Stork) MIDWIFE, and the 6:6:5 one (97 like Outsetter) UPSETTER.
The 3:3:1 UNDERSCORE (SOLL 19) and 4:2:1 OVERSCORE (SOLL 21) refer to a score being 20. The Underscore's 6:1:1 semi-dual is the NURTURER. The 5:1:1 EXORCIST, like the non-coprime 3:3:3 Zombie of MAB 06 inspiring its name, has a move formed of three Ninja moves - or a Ninja and Nimel move, making them hypotenuses of that pair - all at right angles. However the move of the 5:2:1 MONK, a pun on its SOLL being an average month length of 30, is not 3 Camel moves at right angles; once 2 2d moves are placed at right angles the direction at right angles to both is an orthogonal. Other puns are the 5:3:1 ODDFELLOW, the first with three distinct odd coordinates, SOLL 35; 6:3:1 GENOME, whose SOLL of 46 is the number of chromosomes in the human genome; and 6:3:2 HEPTAGRAM, SOLL 49. The 5:4:1 VOTARY has a SOLL of 42, twice the Overscore's by coincidence but thrice the Fortnight's through the 60Â° connection, and so can triangulate.
Cubic pieces sharing each other's SOLLs suit related names. Thus the triangulating 5:3:2 SUSTAINER shares the Nurturer's 38 and the 6:2:1 DANCER the Rector's and Rotcer's 41. The difference often stresses "long, narrow" leaps with a clear longest coordinate versus "short, broad" ones with two equal longest. These include the Elf-Lecturer hypotenuses 5:2:2 LONGPLAYER and 4:4:1 WIDEPLAYER (33), the Fencer-Effarig hypotenuses 5:5:1 FEASTER and 7:1:1 SLIMMER (51), the Exorcist's semi-dual 5:5:2 EXPOUNDER and the 7:2:1 PROPOUNDER (54), the Underscore-Nurturer hypotenuses 5:4:4 NUMBAT and 7:2:2 WOMBAT (57), the 7:3:1 HIGHWAYMAN and 5:5:3 BROADWAYMAN (59), the 7:3:2 AVOWER and triangulating 6:5:1 ENDOWER (62), and the Longplayer's and Wideplayer's semi-duals the 5:5:4 LOREMASTER and 8:1:1 WIREMASTER (66). Note the connection between 5:5 and 7:1 in pairs with SOLLs 51, 54, 59, and 99. Applying this to the Loremaster, or a similar connection between 7:4 and 8:1 to the Wiremaster, gives a third piece with SOLL 66, the 7:4:1 VIREMASTER. To vire is to legitimately reallocate funds from one account (often but not always a contingency account) to another for the same development.
For longer leaps Numbat and Wombat are a jumping-off point, taking other small marsupials as well as rodents smaller than the already-used Squirrel and specific kinds of bat. This "mousehole cavalry" includes the 5:3:3 FIELDMOUSE (SOLL 53), 5:4:2 CHIPMUNK (45, 1Â½ times Monk's), 6:5:2 MOLERAT, 7:3:3 GUINEAPIG, 7:4:2 GERBIL (69, 1Â½ times Genome's), 6:5:3 DORMOUSE (70, twice Oddfellow's, and a Lewis Carroll character), 6:6:1 HAMSTER, 7:5:1 PETMOUSE (75, 1Â½ times Epoletna's), 6:5:4 DUNNART, 7:5:2 BANDICOOT, 7:4:4 OPOSSUM or POSSUM (81, 1Â½ times Propounder's though actually an Exorcist-Expounder hypotenuse), 7:5:3 NOCTULE, 6:5:5 FLITTERMOUSE and 7:6:1 PIPISTRELLE (both 86, former the Fieldmouse's semi-dual, note the 5:5 and 7:1), 7:6:2 FRUITBAT. My Random Rodent Chess uses pieces that mutate between those with rodent names. I could find none starting with the right letters for SOLL 66. Bandicoots (two Arbez moves at 60Â°) and Pipistrelles can triangulate on the right cells or a big enough board. All pieces ending in -mouse have plurals ending in -MICE. Applying the 7:4-8:1 link to the Gerbil and Ognimalf gives pieces for which I had to seek more obscure rodent names, eventually settling on the 8:2:1 MUSKRAT and 8:3:1 OCTODONT. The 8:3:2 piece sharing the Dunnart's SOLL of 77 I named after its fellow marsupial the SUGARGLIDER. For the 8:4:1 leaper sharing the Opossum's SOLL of 81 I had run out of marsupials and so echoed Opossum's ending with ULTIMATUM.
As an 8:5:3 leap can comprise two Heptagram leaps at right angles (e.g. +6:+2:-3 and +2:+3:+6), and an 8:7:7 leap two Ultimatum leaps (e.g. +4:+8:-1 and +4:-1:+8) duality is genuine and so I term these leapers HEMEL and LUMEL and the triangulating compounds EHEU (a Latin exclamation of sorrow) and ULURU (indigenous name for Ayers Rock). Hemels can triangulate, and paradoxically as well as being the Ultimatum's dual the Lumel is the Opossum's semi-dual. Coordinates of 8 and 6 give reversed names in the same manner as those of 4 and 3, resulting in the 8:6:1 WACAM, 8:6:3 DRIBERYL, 8:6:5 LIAMNIAHC, and 8:7:6 YAWANUR.
The Rotcer, Slimmer, Wombat, Numbat, and Guineapig have the semi-duals 8:3:3 ROOTLER, 7:7:2 SKIMMER, 7:7:4 WORRIER, 8:5:5 TINKERER (the Nurturer prevents used of Nu-, and Ti- will never be used for a remainder-1 leaper), and 7:7:6 GRUMBLER. The Longplayer-Loremaster, Wideplayer-Wiremaster, Rotcer-Rootler, Fieldmouse-Flittermouse, Slimmer-Skimmer, and Broadwayman-10:3:3 pairs each have one coprime hypotenuse: the 7:7:1 LOUNGER, 7:5:5 WHINGER, 7:7:5 ROPER, 8:8:1 FILCHER, 8:8:5 SHIRKER, and 8:8:7 OBFUSCATOR. Along with the 7:7:3 HOBBLER, 7:6:6 ELOPER (SOLL 121, square of Elf's), and 8:8:3 EQUIVOCATOR these complete the set of pieces with a repeated coordinate, which may be summed up as follows:
Pieces with SOLLs divisible by nine can often be formed of two or three moves in Ninja directions at right angles. As well as the Nimel and Exorcist these include the Chipmunk as 2[2:1:2]+[1:2:-2], Expounder as 2[2:2:-1]+[2:-1:2]+[-1:2:2], Propounder as 2[2:1:2]+[1:2:-2]+[2:-2:-1], Opossum as 2[2:2:-1]+2[2:-1:2]+[-1:2:2], Ultimatum as 2[2:1:2]+2[1:2:-2]+[2:-2:1], Clinger as 3[2:1:2]+[1:2:-2], Hogger as 3[2:2:1]+[2:-1:-2], Lounger as 3[2:2:-1]+[2:-1:2]+[-1:2:2], Whinger as 3[1:2:2]+[2:-2:1]+[2:1:-2], Bystander as 3[2:1:2]+2[1:2:-2], and Lumel as 4[1:2:2]+[2:1:-2]+[2:-2:1]. Note that they have Ninja leaps in the same proportions that the Knight, Sexton, Sexton, Ninja, Ninja, Camel, Camel, Elf, Elf, Zebra, and Nimel have Wazir steps, making the Oppossum and Ultimatum "Ninjas squared". Stretching it a bit more, a piece whose moves can be formed of m m:n:n leaps in one direction and n 2n:m:m leaps in another at right angles can be seen as the m:n:n leaper squared. Thus the Ninja as a [1:1:1]+[-2:1:1] leaper is a "Viceroy squared and "the Eloper as a 3[3:1:1]+[-2:3:3] leaper an "Elf squared".
These pieces are unavailable on Pentagonal boards and only those with shorter coordinates 1:1 - Sexton, Elf, Nimel, Exorcist, Nurturer, Slimmer, Wiremaster - on Pentagonal-prism ones. Even those exist only on boards with more levels than the longest coordinate, where they are bound to one in that coordinate cells of stacks of rank or file diagonals.
How does Shogi's Forward-only (FO) concept extend to 3 coordinates? The simplest approach is to restrict the forward coordinate to the longest or equal-longest. If two coordinates are equal shortest the piece, like 2d FO pieces in 3d, has 4 moves from the back row; otherwise it has 8. The 2:2:1 DISGUISE - note a different initial from 2d FO pieces - gives a 4:1:1 DUMP and combined (12-direction) DANDYMAN (plural DANDYMEN). In Lewis Carroll's Pig Tale, the frog eventually feels "as dismal as a dump". Likewise the 6:3:2 OCCULT gives an 8:5:3 OUMP and combined OANDYMAN (plural OANDYMEN). Others are the 2:1:1 SHOVEL, 3:1:1 CLOAK, 3:2:2 FOIL, 3:3:1 CEDILLA, 4:2:1 ACCENT, 3:3:2 LESSON, 5:1:1 STAKE, 5:3:1 QUIRK, 5:4:1 ACCEPTANCE, 6:2:1 GRACE, 5:3:3 MEADOW, 6:3:1 CHROMOSOME, 6:4:1 BIRTH.
Name reversals in 4:3 for 5:0 substitutions are maintained with EPIRTS, ENIV, HCTOLB, ALLERBMU, ETSAH, ESON, TELLAM, and ROTAGIRRI. Likewise in 8:6 for 10:0 ones with HTMRAW, REHTIZ, and LLEY. From the Huckster's Tray I derive the 6:6:1 FRAY (which means to erode as rodents do). A more general extrapolation from 2d FO leapers is the 3:2:1 FORTHELM. Where symmetric names are related I maintain this for FO ones: 5:2:1 FRIAR and 5:4:2 CHIPFRYER, 5:2:2 LENGTH and 4:4:1 WIDTH along with 5:5:4 OUTPUT/8:1:1 INPUT/7:4:1 THROUGHPUT, 6:1:1 RUNAROUND and 5:3:2 SUBORDINATE, 5:5:1 GIRTH and 7:1:1 LANK, 5:5:2 TALE and 7:2:1 RANT, 5:4:4 MUNCHER and 7:2:2 MOWER, 7:3:1 HEIGHT and 5:5:3 BREADTH, 7:3:2 FATE and 6:5:1 RITE. From Muncher and Mower I extrapolate the 6:5:2 LOOMER, 7:3:3 NIGGLER, 7:4:2 REGULAR and 8:2:1 SUMMONER, 7:5:1 TEMPTER, 8:3:1 JAW, 6:5:4 DENUDER and 8:3:2 GUSHER, 7:5:2 NABBER, 7:4:4 SOAPER, and 8:3:3 TORTURER.
FO versions of bat-themed pieces are the 7:5:3 GLOOM of the night from which the name Noctule comes, 6:5:5 ARIA from the opera Die Fledermaus, 7:6:1 PIPSQUEAK sharing the symmetric piece's first 3 letters, and 7:6:2 TREE where fruitbats roost. As the Ultimatum is a "Ninja squared" the FO Ultimatum, Lumel, and Uluru follow the pattern of integer-length square-board leapers and their offshoots as the DASTE, DARDNESS, and DEADMAN. FO "Feeble Fringe" pieces are the 7:5:4 GRASP and 8:5:1 GREED, 8:5:2 FASHION, 7:6:3 QUIVER, 6:6:5 JIBE, 7:5:5 INLET and 7:7:1 OUTLET, 7:6:4 INVIGILATOR, 8:5:4 STAGGER, 7:7:2 FILM, 7:7:3 LIMP, 7:6:5 DROOP, 7:7:4 NERVE, 8:5:5 DEN, 8:7:1 PLEA, 8:7:2 STANCE, 7:6:6 LADDER, 8:7:3 STARE, 7:7:5 TWINE, 8:8:1 FRAUD and 8:7:4 PLOT, 7:7:6 GRIPE, 8:8:3 PAUSE, 8:7:5 MESS, 8:8:5 EXCUSE, 8:8:7 OBSTACLE.
These pieces are unavailable on Pentagonal and Pentagonal-prism boards.
For compounds of two oblique pieces, at least one with three nonzero coordinates, I group endings as with both compounds having a zero coordinate. Knight+Sexton=CHURCHWARDEN, Camel+Sexton=TREASURE, Helm+Shovel=PILLAR, Hump+Shovel=MOLEHILL, Sexton+Ninja=OBERON (oblique Baron, from ratio of SOLLs), Sexton+Nimel=DUQUELLE (French relative pronoun from Ducal ratio of SOLLs), Shovel+Disguise=AIRSPACE, Shovel+Dump=COMPACTOR, Knight+Ninja=SAMURAI (higher-rank Japanese warrior), Camel+Ninja=MERCHANT, Helm+Disguise=CREST (a heraldic device on top of a helmet), Hump+Disguise=PACKAGE. The last four give Knight+Nimel=COMERCHANT, Camel+Nimel=COSAMURAI, Helm+Dump=COPACKAGE, Hump+Dump=COCREST. As in MAB 03, the Co- piece is always the one with the longest-leaping component. A one-off back-inherited from hex-prism boards is Fieldmouse+Numbat=HEDGER, with its FO version HEADLOCK - together with its dual Flittermouse+Tinkerer=COHEDGER. Here are the piece images for the Churchwarden, Oberon, and Samurai:
Compounds of the Ninja/Nimel and Ultimatum/Lumel extrapolate from 2d counterparts: Ninja+Ultimatum=DOVERCRAFT, Nimel+Ultimatum=DAJJ, Ninja+Lumel=CODAJJ, Nimel+Lumel=CODOVERCRAFT, Disguise+Daste=DOTSPUR, Dump+Daste=DARDSHIP, Disguise+Dardness=CODARDSHIP, Dump+Dardness=CODOTSPUR. For additional compounds with similar relationships between SOLLs the jumping-off point is Epoletna compounds, which inherit names displaced from Antelope compounds by the new H- ones: Knight+Epoletna=SLEIPNIR (mythical 8-legged horse), Camel+Epoletna=GOUM (convoy of families travelling by camel). To these I add Fortnight+Heptagram=MENHIR (a standing stone as used in occult timekeeping), Fortnight+Hemel=DACORUM (a district whose main town is Hemel Hempstead), Ninja+Opossum=OPHIR (city mentioned in Masefield's Cargoes), Nimel+Opossum=OPPROBRIUM, Elf+Eloper=ELIXIR (a magic potion), Lecturer+Eloper=ELYSIUM (the afterlife of Classical Greek heroes). For exceptionally large 3d boards I can add Arbez+Zoetrope=ABATTOIR and Arbez+Zomel=ARBORETUM, both names alliterating on the Arbez component. I have yet to devise names for corresponding FO pieces.
Compounds of semi-duals share the endings of those of true duals. Thus Elf+Lecturer=LEFANU (surname of woman well known in British serious music circles), Fencer+Effarig=FEU (French for fire), Underscore+Nurturer=NUNCHAKU (a ninja weapon), Exorcist+Expounder=XANADU, Longplayer+Loremaster=LOWENBRAU (a kind of beer), Wideplayer+Wiremaster=WINTHRU (short for win through), Rotcer+Rootler=RONDEAU, Fieldmouse+Flittermouse=FICHU, Slimmer+Skimmer=SHIATSU (a kind of massage), Wombat+Worrier WOUWOU (a species of gibbon), Numbat+Tinkerer=TINAMOU (a partridge-like bird). Likewise compounds of pieces simply named as duals, so that Overscore+Votary=VOUDOU, Oddfellow+Dormouse=DROPTHRU (short for drop through), Chipmunk+Clinger=CISEAU (French for chisel), Nosrap+Onlooker=NOSFERATU, Muskrat+Muddler=MILIEU. Guineapig+Grumbler was a puzzler as I had already used Guru, but then I realised that I could have a name ending with -gu: DEGU, like Guineapig a kind of rodent. Many of the corresponding FO pieces are named after nationalities of various eras: Length+Output=LOCRIAN, Quirk+Sleep=SCYTHIAN, Meadow+Aria=MACEDONIAN, Mower+Nerve=MORAVIAN, Eson+Stare=ESTONIAN, and Summoner+Initiate=MAURETANIAN. Some are prefixed men: Cloak+Lesson=CLANSMAN (person sharing a surname), Foil+Hctolb=FISHERMAN, Cedilla+Runaround=CRACKSMAN (a safe breaker), Accent+Acceptance=AXEMAN, Stake+Tale=STATESMAN, Lank+Film=LINESMAN. Their plurals end in -MEN. Allerbmu+Torturer is the lucky charm TALISMAN (plural TALISMANS), Chipfryer+Grasp CHIPPAN, Muncher+Den the modern artist MONDRIAN, and Niggler+Gripe GREGORIAN.
Semi-duals are also paired for the co- prefix. Knight+Elf=ELAND (an ungulate), Camel+Elf=GENIE, Helm+Cloak=WREATH (for holding a helmet's mantling in place), Hump+Cloak=BULGE thus gives Knight+Lecturer=COGENIE, Camel+Lecturer=COELAND, Helm+Lesson=COBULGE, Hump+Lesson=COWREATH. Likewise Ninja+Elf=NEARTEN (which 9 and 11 both are), Elf+Nimel=ALLURE, Disguise+Cloak=LASCAR (an eastern sailor, and alluding to FIDE players Edward and Emmanuel Lasker), Cloak+Dump=GOODWILL give Ninja+Lecturer=COALLURE, Nimel+Lecturer=CONEARTEN, Disguise+Lesson=COGOODWILL, Dump+Lesson=COLASCAR. Another quartet involving the Elf reuses the Samurai endings: Sexton+Elf=PERI (a type of fairy), Sexton+Lecturer=LIEUTENANT (a junior army offficer), Shovel+Cloak=QUEST, Shovel+Lesson=SALVAGE. I do likewise with the Overscore and Votary. As their SOLLs have the same ratio with the Fortnight as the Ninja and Nimel do with the Sexton I use the same endings: Fortnight+Overscore=PONTOON (a card game name deriving from the French for 21), Fortnight+Votary=ROUELLE (a type of spur), Forthelm=Accent=OUTFACE (as card players may try to do), Forthelm+Acceptance=ROTATOR. Finally it seems logical to make Arbez+Effarig NEDRAWEMAG, Arbez+Epoletna TUOWARD, and Effarig+Epoletna ELLESIG (Gamewarden, Drawout, and Giselle reversed). Fortuitously no previously devised piece starts either Nedra-, Tuodn-, or Elles-, nor any relevant piece end -ag, -es or -ig. FO versions are RALLOC, TEJ, and ROTAVELE.
Of the compound symmetric pieces the Treasure, Duquelle, Cosamurai, Coeland, Conearten, Levant, and Rouelle inherit their components' bindings. The Samurai, Eland, and Nearten are unbound and colourswitching. The rest are neither bound nor switching - the Genie, Allure, Morgai, and Lefanu because, like the Governor in MAB 01: Constitutional Characters, they combine independently-bound components. Binding and switching extrapolate to FO pieces in the usual way.
These pieces are unavailable on Pentagonal boards and only compounds both of whose components have shorter coordinate 1 or 1:1 - Churchwarden, Treasure, Duquelle, Comerchant, Cosamurai, Eland, Genie, Allure, Peri - on Pentagonal-prism ones. Even those exist only on boards with more levels than the longer coordinate, and move exactly one column at a time.
Where a simple leaper's name is 5 letters or less, adding -rider gives long-range pieces such as NINJARIDER, ELFRIDER, CLOAKRIDER, FOILRIDER. Otherwise -rider replaces the sixth letter onward to give SEXTORIDER, FORTNRIDER, FENCERIDER, LECTURIDER, SHOVERIDER, DISGURIDER, FORTHRIDER, LESSORIDER.
Where a compound piece is a pre-existing word, the same rules apply to give ELANDRIDER, GENIERIDER, CRESTRIDER, BULGERIDER, CHURCRIDER, TREASRIDER, PILLARIDER, MOLEHRIDER, OBERORIDER, AIRSPRIDER, SAMURRIDER, MERCHRIDER, PACKARIDER. Where it is its dual's name prefixed with Co-, however, suffixing and curtailment is applied before prefixing to allow up to five letters between prefix and suffix. This gives the likes of COELANDRIDER, COGENIERIDER, COBULGERIDER.
These pieces are unavailable on Pentagonal and Pentagonal-prism boards.
NotesI welcome additions or improvements, but please note how such groups of compound name endings as -elle/-on/-or/-ace, -ut/-in/-et/-al, and -en/-ure/-ar/-ill are preserved, and no two compounds of the same simple piece have the same ending. This is done bearing in mind mixed-range and part-symmetric oblique compounds, which my later article MAB 07: When Beasts Collide covers. Pieces mixing radial and oblique directions have their own article, MAB 08: Diverse Directions. MAB 09: Mighty Like a Rose covers Crooked riders of many of this page's pieces, and Curved riders of triangulating ones. Oblique pieces specific to a hex geometry have their own article, MAB 14: Oddly Oblique. MAB 16: Diverging Further covers divergent pieces in oblique directions, 2d and 3d.
As the next compounds up with SOLL ratios of 1Â½ and 3 are Ninja and Nimel compounds just as the first, the Oberon/Duquelle/Airspace/Compactor, are they require different endings. These and other longer-leap 3d oblique compounds with simple SOLL ratios have their own article, MAB 18: Complex Pieces with Simple Ratios.
Triaxial Qi's 3d analogues to stepping Knights again reinforce the convention of Shogi's narrow meaning of "forward". One kind of stepping Sexton makes a Wazir and a Viceroy step in one move, another makes two steps in different Ferz directions. A stepping Ninja makes a Ferz and a Viceroy step. Again moves comprising only forward steps are more forward than sideways.
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By Charles Gilman.
Web page created: 2007-12-23. Web page last updated: 2013-11-02