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# Man and Beast 20: Far From Square

MAB 10: The Hybrid Diagonal introduced radial, and MAB 14: Oddly Oblique both singly and doubly oblique, pieces specific to hex geometries. Meanwhile MAB 09: Mighty Like a Rose and MAB 13: Straight and Crooked Moving added pieces following non-Straight paths, including a few non-Straight hex-radial pieces. This article extrapolates from them to non-Straight hex-oblique pieces and further radial ones. It also extends the concepts of MAB 12: Alternative Fronts and MAB 16: Diverging Further to hex directions.

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

Curved riders share the basic leaper's binding, if any. Names can be extrapolated two ways from the square board, but fortunately so can moves. 60Â° Curved pieces like the Finch and Rabbi, in a 6-leap circuit, reverse the first 3 letters or 2 consonants, whichever sounds better if the two differ, as for square-cell pieces. The NESNIGHT (SOLL 7), RUAOCHS (13), TSUDENT (19), EVORSCORE (21), WENLYWED (31), OOGSE (37), RABNOWL (39), and PEHTAGRAM (49, not to be confused with Pentagram) are duals of the cubic Roftnight, Abrez, Usutainer, Tovary, Ednower, Ongimalf, Nabdicoot, and Mehel. A piece can also alternate between two angles adding up to 60Â°, 12 leaps making a full circuit, just as the Rose's add to 90Â° with an 8-leap circuit. For the shortest-range of these prefixing the Rose as I do the plain Knight gives SENROSE and extrapolates to AURROSE, STUROSE, OVEROSE, NEWROSE, et cetera.

These pieces have compounds with each other and with Straight riders. Sennirider+Nesnight=NESNIRIDER, Sennirider+Senrose=SENRORIDER, Nesnight+Senrose=NESROSE, and the compound of all three is NESRORIDER. Likewise SOLL 13 gives the RUAOCRIDER, AURRORIDER, RUAROSE, and RUARORIDER. Where a compound of two Straight pieces is named, so is that of their Curved riders. Thus Rabbi+Nesnight=PESRECHAUN, Finch+Ruaochs=RUASHAL, Rabbi+Rose+Nesnight=NACTERER, Nesnight+Macel+Ruaochs=PACERER. Crossover compounds include Rook+Nesnight=SEASERANGER, Viceroy+Nesnight=SEPREMALLOW, Wazir+Ruaochs=AURSHMALLOW, Unicorn+Ruaochs=RAVALRANGER, Finch+Sennirider=SEASEHARRIER, Rabbi+Aurochs=SEPREWARBLER.

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2d Crooked hex riders can be exact 60Â° and 120Â° ones like the Girl- and Range-hexers, and nÂ°/(120-n)Â°/(120+n)Â° ones like the flyers and sidlers of square-cell leapers. The SENNIHEXER, AUROCHEXER, STUDEHEXER, and OVERSHEXER have LONG-, turning exactly 60Â° whose Overscore, Barnowl, Bettong, and Sennight EMDs reflect SOLL ratios of 3; SHORT-, turning exactly 120Â° whose EMDs are the leapers' own directions, or both. Compounds with Straight riders substitute -RACER so that Sennirider+Longsennihexer=LONGSENNIRACER. Each leaper has three flyers, orthogonal-EMD Crooked riders, the Mid- prefix for the angle nearest 90Â°. Examples are (rounded to the nearest degree) 38Â° LONG-/82Â° MID-/158Â° SHORT-SENNIFLYER, 28Â° LONG-/92Â° MID-/148Â° SHORT-AUROCFLYER, 47Â° LONG-/73Â° MID-/167Â° SHORT-STUDEFLYER, and 22Â° LONG-/98Â° MID-/142Â° SHORT-OVERSFLYER. Instead of two sidlers in 2d for want of a standard diagonal (SD) there are three Crooked riders with a nonstandard diagonal (the pure-hex one, abbreviated to ND) EMD. The suffix -SUPPORTER alludes to the Unicorn's rÃ´le in the Scottish royal arms. Again rounded are a 22Â° LONG-/98Â° MID-/142Â° SHORT-SENNISUPPORTER, 32Â° LONG-/88Â° MID-/152Â° SHORT-AUROCSUPPORTER, 13Â° LONG-/107Â° MID-/133Â° SHORT-STUDESUPPORTER, and 38Â° LONG-/82Â° MID-/158Â° SHORT-OVERSSUPPORTER. Overssupporters share turning angles with Senniflyers and vice versa. Unprefixed flyers and supporters are compounds of Long, Mid, and Short while compounds with Straight riders replace -flyer with -officer, or -supporter with -parade - alluding to the Cavalcade. Thus Sennirider+Midsenniflyer=MIDSENNIOFFICER, Aurocrider+Shortaurocsupporter=SHORTAUROCPARADE.

Hex-prism boards give Square-cell leapers new Crooked riders. The Knight is a special case: as the cubic Longnightsidler has a Nimelwise second EMD, the hex-prism Longnightflyer has a hybrid-diagonal one. Hex-prism-specific Crooked riders have further suffixes. Hex-orthogonal-EMD ones take -TOWER, from the Staunton Rook's shape and Air Traffic Control towers. ND-EMD ones take the previous paragraph's -SUPPORTER. Others take -PLANER indicating an EMD in a rectilinear plane, or -PRISONER indicating a hex-prism-specific EMD. This puns on prism as well as alluding to imprisonment in a tower. The -tower and -prisoner angles with the same prefixes always add to 180Â°, likewise the -supporter and -planer ones. Pairs include the 78Â° OUTERNIGHTPLANER (EMD SD) and 102Â° OUTERNIGHTSUPPORTER, 46Â° INNERNIGHTPLANER (EMD Giraffewise) and 134Â° INNERNIGHTSUPPORTER, 26Â° INNERNIGHTPRISONER (EMD Underscorewise) and 154Â° INNERNIGHTTOWER, 70Â° OUTERCAMELSUPPORTER and 110Â° OUTERCAMELPLANER (EMD Zebrawise), 57Â° OUTERCAMELPRISONER (EMD Vampirewise) and 123Â° OUTERCAMELTOWER, the 32Â° INNERCAMELPLANER (EMD Flamingowise) and 148Â° INNERCAMELSUPPORTER, 18Â° INNERCAMELPLANER (EMD 6:r3-wise) and 162Â° INNERCAMELTOWER, 88Â° OUTERZEBRASUPPORTER and 92Â° OUTERZEBRAPLANER (EMD Antelopewise), 57Â° INNERZEBRAPLANER (EMD Camelwise) and 123Â° INNERZEBRASUPPORTER, 59Â° OUTERZEBRAPRISONER (EMD Fieldmousewise) and 131Â° OUTERZEBRATOWER, 32Â° INNERZEBRAPRISONER (EMD Camelwise) and 148Â° INNERZEBRATOWER, 66Â° OUTERGIRAFSUPPORTER and 114Â° OUTERGIRAFPLANER (EMD Knightwise), 58Â° OUTERGIRAFPRISONER (EMD Ratifierwise) and 122Â° OUTERGIRAFTOWER, 24Â° INNERGIRAFPLANER (EMD Bitternwise) and 156Â° INNERGIRAFSUPPORTER, 14Â° INNERGIRAFPRISONER (EMD :r3-wise) and 166Â° INNERGIRAFTOWER, and many more. The compound of Inner- and Outer- pieces is unprefixed, with the special cases NIGHTPRISONER=Longnightflyer+Innernightprisoner and NIGHTTOWER=Shortnightflyer+Innernighttower. SD pieces lack separate Inner and Outer Crooked riders, so the 76Â° BOYPLANER, ELEPHPLANER, TRIPPPLANER... (EMD Knightwise) and 104Â° BOYSUPPORTER, ELEPHSUPPORTER, TRIPPSUPPORTER... and the 41Â° BOYPRISONER, ELEPHPRISONER, TRIPPPRISONER... (EMD Foalwise) and 139Â° BOYTOWER, ELEPHTOWER, TRIPPTOWER... need no prefixes.

Hex-prism-specific leapers have one Crooked rider suffixed -flyer whose EMD is the interhex orthogonal, and one suffixed -COMBER whose EMD is the hex coordinate's direction. Hybrid-diagonal and singly oblique pieces also have a single tower, supporter, planer, and prisoner. Singly oblique pairs include the 83Â° RUMBATOWER and 97Â° RUMBAPRISONER (EMD Foalwise), 60Â° RUMBACOMBER and 120Â° RUMBAFLYER, 51Â° RUMBAPLANER (EMD Zebrawise) and 129Â° RUMBASUPPORTER, 82Â° FOALFLYER and 98Â° FOALCOMBER, 69Â° FOALPRISONER (EMD Underscorewise) and 111Â° FOALTOWER, 38Â° FOALPLANER (EMD Antelopewise) and 142Â° FOALSUPPORTER, 60Â° PREFEFLYER and 120Â° PREFECOMBER, 51Â° PREFEPRISONER (EMD 6:r3-wise) and 129Â° PREFETOWER, 29Â° PREFEPLANER (EMD Knightwise) and 151Â° PREFESUPPORTER, 67Â° BAKERTOWER and 113Â° BAKERPRISONER (EMD hybrid diagonal), 57Â° BAKERPLANER (EMD Camelwise) and 123Â° BAKERSUPPORTER, 32Â° BAKERCOMBER and 148Â° BAKERFLYER, et cetera. Most doubly oblique leapers have three towers/supporters/planers/prisoners plus two further pieces each with hex and hex-prism EMDs, respectively suffixed -DIVER and -CLIMBER. Special cases are a 90Â° HEFFADUELLER with both orthogonal and hybrid-diagonal EMDs rather than separate Midheffa-prisoner/-tower, 74Â° ELFCOMBER (EMD Sennightwise and Foalwise) and 106Â° ELFFLYER doubling as Midelf-prisoner/-tower, and 31Â° FORTNCOMBER (EMD Aurocwise and Bakerwise) and 149Â° FORTNFLYER doubling as Longfortnprisoner/Shortfortntower. More typical are the 76Â° MIDHEFFAPLANER (EMD Knightwise) and 104Â° MIDHEFFASUPPORTER, 72Â° LONGHEFFADIVER (EMD Overscorewise) and 108Â° SHORTHEFFACLIMBER (EMD Elfwise), 56Â° LONGHEFFACLIMBER (EMD Daverscorewise) and 124Â° SHORTHEFFADIVER (EMD Sennightwise), 47Â° LONGHEFFASUPPORTER and 133Â° SHORTHEFFAPLANER (EMD Knightwise), 41Â° HEFFACOMBER and 139Â° HEFFAFLYER, 20Â° LONGHEFFAPRISONER (EMD Vampirewise) and 160Â° SHORTHEFFATOWER, 87Â° SHORTELFCLIMBER (EMD Germinatorwise) and 93Â° LONGELFDIVER (EMD Overscoerwise), 82Â° LONGELFTOWER and 98Â° SHORTELFPRISONER (EMD Underscorewise), 77Â° LONGELFSUPPORTER and 103Â° SHORTELFPLANER (EMD Giraffewise), 63Â° MIDELFPLANER (EMD SD) and 117Â° MIDELFSUPPORTER, 47Â° LONGELFCLIMBER (EMD Quanderscorewise) and 133Â° SHORTELFDIVER (EMD Sennightwise), 30Â° LONGELFPLANER (EMD Rectorwise) and 150Â° SHORTELFSUPPORTER, 17Â° LONGELFPRISONER (EMD Fieldmousewise) and 163Â° SHORTELFTOWER, 87Â° MIDFORTNPLANER (EMD Satyrwise) and 93Â° MIDFORTNSUPPORTER, 84Â° MIDFORTNPRISONER (EMD Vampirewise) and 96Â° MIDFORTNTOWER, 67Â° LONGFORTNDIVER (EMD Barnowlwise) and 113Â° SHORTFORTNCLIMBER (EMD Fencerwise), 58Â° LONGFORTNCLIMBER (EMD Fieldmousewise) and 122Â° SHORTFORTNDIVER (EMD Aurocwise), 44Â° LONGFORTNSUPPORTER and 136Â° SHORTFORTNPLANER (EMD SD), 41Â° LONGFORTNTOWER and 139Â° SHORTFORTNPRISONER (EMD Foalwise), and 27Â° LONGFORTNPLANER (EMD Storkwise) and 153Â° SHORTFORTNSUPPORTER. Again the unprefixed piece is the compound of all prefixed ones. Note that the Heffadueller is a component of both HEFFAPRISONER and HEFFATOWER, the Elfcomber of the ELFPRISIONER, the Elfflyer of the ELFTOWER, the Fortncomber of the FORTNPRISONER, and the Fortnflyer of the FORTNTOWER.

Compounds between the -rider and the -tower, -comber, -prisoner, -planer, -climber, and -diver substitute yet another suffix, retaining the Crooked piece's prefix if any. Anyone who can better -HOUSER, -KEEPER (from beekeeper), -ESCAPER, -JOINER (from carpentry), -BRANCHER, and -PLUNGER respectively (particularly the desperate last two) is welcome to try.

Curved+Corkscrew pieces of a certain kind on hex-prism boards are worthy of names as they are used here, As they are so numerous I prefix the Curved component with CHAF- on the basis of this making Finch+Boysextupet CHAFFINCH. Others are Rabbi+Rumbasextuplet=CHAFRABBI, Cohen+Landlsextuplet=CHAFCOHEN, Shammes+Cooksextuplet=CHAFSHAMMES, and Contrashammes+Contracooksextuplet=CHAFCONTRASHAMMES.

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30Â° orthogonal/ND ones alternators (alternation, EMD) include the SENRHINO (Duke, Sennight), ORYX (Vicbaba, Aurochs), APPRENTICE (Wazzock, Student), OVERLINE (Bullfrog, Overscore), LOVER (Viceroy+Cobbler, Newlywed), GOON (Warmer, Goose), BARNSTORMER (Eft, Barnowl), PRIZEJOYSTICK (Viceroy+Quibbler, Prizemouse), HEPTAGON (Dazzler, Heptagram), GAMBLER (Viceroy+Bitrebuchet, Bettong), and ENFOLD (Wazir+Corpse, Entrap). Side-saddle versions turning 60Â° are the SIDESENRHINO (Wazbaba, Sennight), SIDEORYX (Watcher, Aurochs), SIDEAPPRENTICE (Toad, Student), SIDEOVERLINE (Cordwainer, Overscore), CORNEROVERLINE (Vinnock, Overscore), et cetera. Like 45Â° square-board alternators both groups have Curved as well as Crooked forms. 90Â° orthogonal/ND alternators exist on hex boards but have extra moves on hex-prism ones. Those with th same EMDs as 30Â° ones take the latter's name preceded by ANGLE-. Thus to the ANGLESENRHINO (Vicbaba, Sennight), ANGLEORYX (Wazzock, Aurochs), ANGLEAPPRENTICE (Viceroy+Cobbler, Student), ANGLEOVERLINE (Eft, Overscore), ANGLELOVER (Dazzler, Newlyewd), ANGLEGOON (Eunuch+Quibbler, Goose), ANGLEPRIZEJOYSTICK (Cobbler+Zombie, Prizemouse), ANGLEHEPTAGON (Wazir+Corpse, Heptagon), and ANGLEGAMBLER the hex-prism board adds respectively a Foal, Baker, Underscore, Offscore, Vampire, Cormorant, Fieldmouse, Sceptic, and Numbat EMD to give overall Horsiness, Barmaid, Cotautness, Openness, Covagueness, Cooceanus, Cooperahat, Homeliness, and Cotitration EMDs. Alternators without a corresponding non Angle- piece include the ARCHIMEDES (Duke, Dabbaba), DAMOCLES (Bullfrog, Eunuch), MOSES (Viceroy+Quibbler, Semming), MAIMONIDES (Warmer, Semming), and HERACLES (Quibbler+Zombie, Rharolais). To these pieces hex-prism adds respectively a Rumbaba, Prefect, Spectre, Golem, and Ratifier EMD. Names are after a war-machine inventor, a sycophantic attendant, a giver of laws including a seven-day week, a later folloewr of his religion, and a fighter of large animals.

The xyrixa geometry adds a 73Â° Wazir/Viceroy alternator with a Knightwise EMD, termed EOHIPPUS after the first known ancestor of horses but not of rhinos or tapirs. It also adds 90Â° Wazir/Sexton, Wazir/Elf, and Nimel/Nimel alternators: the SENVASCALER, LEASESCALER, and NIMELDUELLER.

Hex-prism boards add further alternators. A Prince alternator turning 69Â° has a hybrid-diagonal EMD. As such alternations at other angles add or remove a horn - Rhino with Knight EMD, Tapir with Unicorn EMD - this latest one is a POLLARD, meaning a hornless member of a usually (two-)horned species. 69Â° turns between non-coprime leaps give (alternation, EMD) the ENT (Waffle, Elf), and MOERITHERE (Fezbaba, Heffalump). Marquis alternators are the 90Â° TITANOTHERE, naturally sharing the Siderhino's Knightwise EMD; 60Â° CHALICOTHERE, EMD Foalwise; and 41Â° BALUCHITHERE, EMD Heffalumpwise, named after extinct animals of the horse/rhino order. 52Â° Baron, 28Â° and 80Â° Landlord, and 30Â° and 60Â° Bellman alternators are AARDVARK, PIXIE, HYPERSENRHINO, MILLER, and VICUNA for their Heffalumpwise, Elfwise, Sennightwise, Bakerwise, and Camelwise EMDs. The 69Â° Landlord alternator's EMD is even steps of the SD. For this ALCHEMIST echoes both the scale of transformation and the period of Bishops replacing Elephants (Alfils), with the bonus of the Arabic Al- prefix. 90Â° orthogonal/pure-hex alternators (with EMD) include the SEASESCALER (Heffalump), AURSHSCALER (Fortnight), SUASESCALER (Calibrator), OVESHSCALER (Tutor), SEGIOSCALER (Elf), RARPESCALER (Fencer), SUGIOSCALER (Hybridiser), VOSBASCALER (Pentagram).

The MAB 13 prefixes WOMAN-, MAN-, and PAIR- indicate the usual straight-piece compounds. Womanside-, Manside-, Womancorner-, and Mancorner- become MATRI-, PATRI-, SORORI-, and FRATRI-.

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Bent pieces starting with a Rumbaba step turn 41Â° to continue as a Rook, 18Â° as a Bishop, and 30Â° as a Unicorn, and each trio are listed in that order. Following the themes of others with the same long-range stage they are respectively the HYDRA, STARGAZER, and BUCEPHALUS. Compounds with Rook/Bishop/Unicorn themselves are SPHINX, MAGUS, and EQUERRY - and with the Dicorn NEAPOLITAN, HOROSCOPE, and OXHERD. The LAUNCHER, NECROMANCER, and RESONATER move two steps before turning and their Rook/Bishop/Unicorn compounds are DAMBUSTER, MEDIUM, and DISMANTLER. Pieces whose long-range stage is a Dicorn move (but with the same turns) require some previously unused theme. Having named the Oberon, Puck, Titania from a Shakespeare comedy I turn to his tragedies with a female and male lover respectively for those starting off orthogonal and SD, and one hostile to the relationship for those starting off ND. Thus those moving as a Dicorn after a Wazir/Ferz/Viceroy step are JULIET/ROMEO/TYBALT, their Dicorn compounds CRESSIDA/TROILUS/CALCHAS, and their Rook/Bishop/Unicorn compounds CLEOPATRA/ANTONY/OCTAVIAN. Those moving two steps before turning are DESDEMONA/OTHELLO/IAGO and their own Dicorn compounds OPHELIA/HAMLET/CLAUDIUS.

Compounds of Bent pieces sharing a short-range stage suffix the name of the component not using the hybrid diagonal with the -LINE suffix of MAB 17: Hex Haavies. Thus Gryphon+Romeo=GRYPHONLINE, Simurgh+Tybalt=SIMURGHLINE, Anchorite+Juliet=ANCHORITELINE, Celebrant+Tybalt=CELEBRANTLINE, Farrier+Juliet=FARRIERLINE, Nag+Romeo=NAGLINE, Zephyr+Othello=ZEPHYRLINE, et cetera. Compounds of Bent pieces sharing a long-range stage follow the cubic -sheath/-sack pair, which also work on hex-prism boards but excluding hybrid diagonals. Based on a cross-section of combined routes excluding NDs gives -SHIELD/-STAR, excluding SDs -WAFER/-DICER, and excluding orthogonals -URCHIN/-HEDGE. Thus Gryphon+Hydra=ROOKSHIELD, Simurgh+Hydra=ROOKWAFER, Anchorite+Stargazer=BISHOSHIELD, Celebrant+Stargazer=BISHOURCHIN, Farrier+Bucephalus=UNICOWAFER, Nag+Bucephalus=UNICOURCHIN, Juliet+Romeo=DICORSHIELD, Juliet+Tybalt=DICORWAFER, Romeo+Tybalt DICORURCHIN, Zephyr+Trampoliner=ROOKSTAR, Lama+Necromancer BISHOSTAR, et cetera. Compounds with the Straight piece named likewise move the suffix on from -shield/-star to -TIMES/-TREX, -wafer/-dicer to -EQUAL/-EX, and -urchin/-hedge to -ABSTRACT/-AXE. Thus Rook+Rookshield=Reaper+Hydra=Sphinx+Gryphon=ROOKTIMES, Bishop+Bishoshield=Harvester+Stargazer=Magus+Anchorite=BISHOTIMES, et cetera. Fimbriating a -sheath still adds the -sack, a -shield the -star, a -wafer the -dicer, an -urchin the -hedge, a -plus ther -plex, a -times the -trex, an -equal the -ex, and an -abstract the -axe.

As usual, Contra- puts the long stage first, Double allows either order, and the first five letters of two Bent pieces compounds the first with the Contra- of the second, thus GRYPHHYDRA=Gryphon+Contrahydra. Pieces can also combine two stages with more diverse pairs of radial moves including an HD move, or an HD move and an oblique one, or a radial move and a hex oblique one. Again these can be described with the two stages hyphenated togehe followed by MONSTER.

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Corkscrew pieces such as the RUMBASEXTUPLET, FOALSEXTUPLET, HEFFASEXTUPLET, HEFFADODECLET, ELFSEXTUPLET, ELFDODECLET, PREFESEXTUPLET, BAKERSEXTUPLET, FORTNSEXTUPLET, FORTNDODECLET, FENCESEXTUPLET, and FENCEDODECLET have an interhex-orthogonal CMD. Compounds with the Straight rider drop -upl- from -sextuplet.

Double-Bent pieces top and tail Rook/Bishop/Unicorn moves with Rumbaba steps. Named after mythical dog monsters, ORTHROS and CERBERUS are brothers in Greek mythology, and WENDIGO North American and coyote-based but sounding like Dingo. Others top and tail the Dicorn move with Wazir/Ferz/Viceroy steps. These are named after a related carnivore family: WEASEL, FERRET, and STOAT - the first two for their initials and the third for its heraldic (ermine) associations.

Compounds of both latter types use the usual double-Bent and Switchback prefixes and suffixes. For Double-Bent pieces' Dicorn compounds I resort to the suffix -FORK from the Dilemma theme.

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Hex-specific non-symmetric pieces follow on from MAB 12 and 16. On hex-level boards compounds of the FO piece and its coward are the symmetric piece's ranker and those of the dexter and sinister its filer. On hex-ranked ones those of the chief and base are its leveller, those of the dexter and sinister its columner. Fore-, Hind-, Veering, Backing, Subveering, and Subbacking pieces are not defined for hex-ranked 3d boards.

FO oblique 2d hex pieces have dexters, sinisters, and cowards such as the SENHEDEXTER, RINGSINISTER, and PASTCOWARD moving in the two directions most closely flanking due right, left, and backward respectively, be the flanked direction orthogonal or ND. Hex-level 3d boards do not add chiefs and bases, and hex-ranked ones do so at the expense of the coward and original FO piece. As rankers and filers each have only 4 directions these add up to only 8 of the symmetric piece's 12 directions. The third subset of moves, the 4 most nearly at 45Â° to the straight forward/backward and left/right radials, suit the suffix -QUARTERER as the directions divide the board nearly into quarters. Thus Sennight=SENNIRANKER+SENNIQUARTERER+SENNIFILER. Hex-level 3d boards again add nothing, and hex-ranked ones substitute Sennight=SENNILEVELLER+SENNIQUARTERER+SENNICOLUMNER. Hybrid-diagonal and singly oblique FO pieces' cowards inherit their 8 directions if Glinski-level, 4 if Wellisch-level, 6 if hex-ranked, but dexters and sinisters have 4 directions if Glinski-level and 8 if Wellisch-level or hex-ranked, and chiefs and bases have 6 if either hex-level and 4 if hex-ranked. Examples are RUMCHCOWARD, TRAINDEXTER, OVENCHIEF. The symmetric piece is ranker+filer or leveller+columner, making the Rumbaba RUMBARANKER+RUMBAFILER or RUMBALEVELLER+RUMBACOLUMNER. Yhe symmetric pieces' directions are halved by Fore- for directions above and below the Foreunicorn's, and Hind- above and below the Hindunicorn's. Super- pieces are Wellisch-specific, and -superdexters and -supersinisters Glinskiy-specific, and have destinations above and below the Superhorn's. Likewise -supercowards regarding the Hornsupercoward. Reservists and revisionists work the usual way. Rotating doubly oblique FO pieces retains or substitutes 4 directions, except that hex-ranked cowards retain, and hex-level chief and bases substitute, 12 directions. Examples include RUMTUCOWARD, CLOAKDEXTER, FORTHCHIEF. Again rankers and filers each have only 8 directions, the two adding up to only 16 of the symmetric piece's 24 directions, so these too have quarterers. All three - and Fore-, Hind-, Veering, Backing, Subveering, and Subbacking pieces - have directions above and below the corresponding 2d hex ones. Thus Heffalump is HEFFARANKER+HEFFAQUARTERER+HEFFAFILER or HEFFALEVELLER+HEFFAQUARTERER+HEFFACOLUMNER.

Prefixes halving the symmetric pieces' directions are Fore- for the two most forward and all backward except the two most backward, Hind- for the reverse, Veering for the first left of straight forward and every 60Â°, Backing for the first right of straight forward and every 60Â°, SUBVEERING for the first left of straight and every third direction, and SUBBACKING for the first right of straight forward and every third direction. Crablike combinations of forward and backward move can again go two ways with two ways of naming. The SREN, ARUR, SRTU, ORVE combine an FO pure-hex piece with its -revisionist. Likewise the HREF, ERLF, FROR a doubly-oblique one. Reversing the letters reverses the directions. The SENCRAB, AURCRAB, STUCRAB, OVECRAB, HEFCRAB, ELFCRAB, FORCRAB combine it with its -reservist and -shelterer. -barc again reverses the directions. Thus the Sennight is FORESENNIGHT+HINDSENNIGHT, VEERING SENNIGHT+BACKING SENNIGHT, Senniquarterer+SUBVEERING SENNIGHT+SUBBACKING SENNIGHT, Sren+Senniquarterer+NERS, or Sencrab+SENBARC. As with square boards, Veering and Backing bind pieces to 1 in their SOLL of the board. Quarterers and Subveering/Subbacking pieces tend to be more severely bound still. With 6 pairs of directions instead of 4 FO pieces' -quarterers use the second most forward pair (as FO form of the symmetric piece's quarterer) and -SHELTERERS the second most backward, leaving -reservist and -revisionist for the third most forward/backward. Alongside SUPER- adding an FO piece's -reservist ULTRA- adds its -quarterer and HYPER- both. Fergus Duniho's family of hex Shogis uses an ULTRASENHELM. To complete the compounds, -quarterer plus -reservist is -QUASAR and -shelterer plus -revisionist -SHELVER. These all apply also to doubly-oblique pieces, so that Heffalump is FOREHEFFALUMP+HINDHEFFALUMP, VEERING HEFFALUMP+BACKING HEFFALUMP, or SUBVEERING HEFFALUMP+Heffaquarterer+SUBBACKING HEFFALUMP.

Xyrixa boards reverse the Brook family with "rotated diagonal" pieces moving on the one forward and one backward diagonal but two pairs of same-rank orthogonals. The WFERZ, RBISHOP, WFEARFUL, PPICKET, CARROW, and PBEAR are bound to all of alternate ranks and The DELEPHANT and MSPEAR to alternate Dabbaba bindings. Compounds include the DBARON, DGOVERNOR, BSTEEL, VMODERATOR, BHERETIC, DELK, WFEZZOCK, VWILFUL, KIMAM, CMUTILATOR, CBEHEMOTH, CARBALEST, SBLESSING, PBALLOON, CBUFFOON, and PBOFFIN. On hex-prism boards an orthogonal piece can be rotated by 30Â° about the interhex orthogonal and the hex moves multiplied by root 3. Such pieces are bound to a third of the unrotated piece's binding. Using 2 instead of 1 ND-piece letter gives the VIWAZIR, UNROOK, EUDABBABA (thus distinct from the Edabbaba), PAPOCKET (thus distinct from the Ppocket), SLCANNON, RAPANDA, ZOTREBUCHET et cetera. Prefixes are not required as board orientiation determines piece direction. Compounds include Viwazir+Ferz=BAPRINCE, Unrook+Bishop=GOQUEEN, Unrook+Ferz=HECHATELAINE, Bishop+Viwazir=MOPRIMATE, Viwazir+Cross=JAGOLD, Viwazir+Eudabbaba=VIWAZBABA, Eudabbaba+Elephant=ELALIBABA, Viwazir+Elephant=WIWAFFLE, Ferz+Eudabbaba=FEFEZBABA, Unrook+Elephant=BEINFANTA, Bishop+Eudabbaba=MUINQUISITOR, Slcannon+Arrow=ARTANK, Unrook+Arrow=UNSPARROW, Bishop+Slcannon=BLSAINT, Rapanda+Bear=BAHARLEQUIN, Unrook+Bear=BUCOLUMBINE, Bishop+Rapanda=BUCLOWN, Viwazir+Rumbaba=BEMARQUIS, Unrook+Dicorn=TRMARCHIONESS, Unrook+Rumbaba=DOHOUSEWIFE, Dicorn+Viwazir=RECHAMBERLAIN.

To Moor- pieces a hex-prism board adds Ferzranker+Rumbafiler on Glinski-level, vice versa on Wellisch-level, and Ferzcolumner+Rumbaleveller on hex-ranked, boards. I term all GROUSE, and their riders PHEASANT. The HYRAX, NEUROTIC, BOYCOTT, SIGNPOST, and BADGER have corresponding subsets of the Alderman, Mullah, Picketline, Arrowline, and Bearline moves. Compounds with Moor- pieces are Moorcock+Grouse=PEACOCK, Moorhen+Pheasant=PEAHEN, Moordemon+Hyrax=PEADEMON, Moorpotentate+Neurotic=PEAPOTENTATE, Moormiser+Boycott=PEAMISER, Moorhopper+Signpost=PEAHOPPER, and Moorswitcher+Badger=PEASWITCHER. The Super- prefix is carried over so that the SUPERFERZ and SUPERRUMBABA add remaining Grouse moves to give larger subsets of the Landlord move, SUPERBISHOP and SUPERDICORN remaining Pheasant moves to give larger subsets of the Pontiff move, SUPERPRINCE SUPERKING and SUPERBELLMAN remaining Peacock moves to give larger subsets of the World-general/-ruler move, SUPERQUEEN and SUPERTRICORN remaining Peahen moves to give larger subsets of the Worldrider move, et cetera. In oblique directions the SUPERKNIGHT adds selected Haymaker, and SUPERCAMEL selected Handler, moves. The SUPERFOAL adds only half the relevant plane's Knight moves, and the SUPERBAKER only the other half, with only the SUPERHAYMAKER adding both lots. Likewise the SUPERPREFECT, SUPERGOLEM, and SUPERHANDLER with Camel moves.

Also notable are puppeteers across different groups. The SENNIGHT-FOAL PUPPETEER and vice versa have 12 directions, but alternate between pairs of same-level and of level-changing moves. The likes of the SENNIGHT-HEFFALUMP and FOAL-HEFFALUMP PUPPETEER have 18 directions, alternating pairs with foursomes.

The Moor- pieces' 1 in 2 binding seen as analogue to the standard diagonal is easy to extrapolate to square-board oblique directions. Knight and Camel analogues the CALASH and CAISSON are named after kinds of horse-drawn vehicle. On a Glinski board they are Vicerranker+Sennifiler and Senniquarterer+Aurocfiler. Extrapolations include Senniranker+Studefiler=ZELASH, Aurocquarter+Oversfiler=GILASH, Aurocranker+Goosefiler=NALASH, Oversquarterer+Newlyfiler=ZEISSON, Studequarterer+Barnofiler=SALASH, Underranker+Heptafiler=GIISSON, et cetera. A Wellisch board reverses -ranker and -filer suffixes, but -quarterer ones remain the same. This finally brings me to Chevron oblique analogues.

Rotations of the Calash corresponding to the Inspector for the Moorcock go up from the FO Sergeant and Corporal to CAPTAIN. Those of the Caisson are KAIMAKAN, a historic Turkish military rank. However note that a move across the middle file distorts them. Thus a Captain on a file next to the middle one has its usual moves outward and to the middle file itself, but across it moves to the Dabbaba destinations rather than one Viceroy and one Sennight one. The forward-only version of the Captain, making just the inward Senhelm and outward Saltire move, is the CADET, and that of the Kaimakan, making just the inward Past and outward Senhelm move, the KAFTAN. Captain+Kaimakan is AKOND after a potentate publicised in an Edward Lear poem, and Cadet+Kaftan ACOLYTE after a potentate's underling. These extrapolate to ZEPTAIN+ZEIMAKAN=EZOND, ZEDET+ZEFTAN=EZOLYTE, GIPTAIN+GIIMAKAN=IGOND, GIDET+GIFTAN=IGOLYTE, et cetera. For movement diagrams I show the entire board with examples both left and right of the centreline. The numbers 1 and 2 represent destinations specific to them respectively, and 3 represents destinations common to both. Here are those for the Captain, Kaimakan, Cadet, and Akond:

.

Pentagonal-specific pieces are by nature almost all non-Straight. They do not have an EMD as such and certainly not one defined in terms of a Straight piece's move. These first appear in SerPent Chess, but they behave slightly differently in the geometry of Daniil Frolov's Pentagonal Chess.

The RATTLESNAKE is a Crooked orthogonal, and the BOA a diagonal, piece alternating between the second turnings left and right, but out of 5 instead of 4 or 6. Lewis Carroll's Gardener's Song features a "rattlesnake that questioned him in Greek". On a SerPent board a Rattlesnake can make a series of forward or backward steps along a file orthogonal, a series of sideways steps along a rank orthogonal, or a mixture along a back-right-to-front-left bend orthogonal or back-left-to-front-right scarp orthogonal. On a Frolov board it can move forward and backward shifting by "half a file" every two ranks, or sideways alternating between 3-cell blocks on 2 ranks. On a rotated one it can move sideways shifting by "half a rank" every two files, or forward and backward alternating between 3-cell blocks on 2 files. On a SerPent board a Boa can make a series of forward or backward steps along a file diagonal or a series or sideways steps along a rank diagonal - but not between the two, making it a very weak piece. Only by being able to return from capture, or by a King Swap in the Yang Qi style, can a Boa get to make all possible moves. On Pentagonal-prism boards the Rattlesnake gains a Wazir step up and down, and the Boa all series of diagonal steps rising above and falling below same-level Rattlesnake paths, unbinding it. The NADDER is an orthogonal Curved piece whose move takes either the second turning left at every cell or the second right at every cell, but out of 5 instead of 6. On a SerPent board it encirles any hexagonal block of four cells. On a Frolov one it can encircle a pair of neighbouring cells one directly in front of the other, or slightly surprisingly move along a single rank. On a 90Â° rotated Frolov board it can encircle a pair of neighbouring cells directly side by side, or move along a single file. The UROTHECA is specific to Pentagonal-prism board and makse a series of Viceroy steps rising above or falling below the same-level Boa moves - and again needs to return from capture of undergo an Emperor Swap to be able to make all possible moves. The names are snakes whose initials are the usual abbreviations for Rook/Bishop/Knight/Unicorn, Nadder being an archaic alternative form of adder to give the N. The piece rising above or falling below the Nadder paths is a form of BOYDECUPLET on the SerPent board and a BOYOCTUPLET on the Frolov Pentagonal one.

Compounds - save for Rook+Rattlesnake=RATTLRIDER, Rook+Nadder=NADDERIDER - are named after snakes or snake-based deities with Queen/Marshal/Cardinal/Ace/Chatelaine/Primate initials. Rattlesnake+Boa=QUETZALCOATL, Nadder+Rattlesnake=MAMBA, Nadder+Boa=CONSTRICTOR, Nadder+Quetzalcoatl=APEP, Rattlesnake+Ferz=COBRA, and Boa+Wazir=PYTHON. In 3d additioal pieces are named to give Vicereine/Moderator/Duchess/Governor/Besieger/Heretic initials, and so tend to use more obscure snake names: Rattlesnake+Viceroy=VIPER, Boa+Viceroy the snake variously spelled MOCASSIN or MOCCASIN, Rattlesnake+Urotheca=DIAMONDBACK, Boa+Urotheca=GARTERSNAKE, Urotheca+Wazir=BALANOPHIS, Urotheca+Ferz=HELOPHIS.

FO pieces are named after kinds of movement with Wing/Mitre/Princeling/Helm/Caryatid/Abbot initials. On SerPent boards the WAGGLE follows file orthogonals, the MEANDER file diagonals (including above and below file orthogonals in 3d), and the PROWL both. On a 90Â° rotated Frolov board the HURRY goes forward along the file. Compounds include Waggle+Cross=CALL, Meander+Point=APPROACH. 3d adds pieces with Horn/Virago/Elder/Countess/Missionary/Ram/Debate initials: the HAVER rises above and falls below same-level file diagonals while Waggle+Saltire=VISIT, Meander+Saltire=ENCROACH, Waggle+Haver=CHASE, Meander+Haver=MEET, Haver+Wazir=RUNINTO, Haver+Ferz=DROPINON. Part-symmetric pieces are Rattlesnake+Meander=GOLDPROWL and Boa+Waggle=SILVERPROWL. GOLDRATTLESNAKE adds a Cross, SILVERBOA a Point, BRASSRATTLESNAKE/STEELBOA/SKYQUETZALCOATL a Saltire, SUNRATTLESNAKE an Heir, MOONBOA a Count, GOLDMEANDER a Wazir, SILVERWAGGLE a Ferz, AZUREWAGGLE/JADEMEANDER/COASTPROWL a Viceroy, FORESTMEANDER a Duke, and SEAWAGGLE a Baron to the unprefixed piece.

There is also a Straight alternator, the RECTIFIER starting with the R of Rhino and suggesting straightening things out. This can move as a Prince but can also make a Ferz step preceded or succeeded or both by a Wazir step, all horizontal, on a SerPent board and make a continuous chain of alternating steps right across a Frolov board. Regarding Bent pieces the GRASSSNAKE differs from the Rattlesnake in that the first step has a component up or down one level, and the ANACONDA from a Boaleveller in that the first step lacks its inter-level component and so is a Wazir step.

## Notes

The group of pieces including Grouse and Pheasant excludes Partridge as that is already the derived name of MAB 07's forward-only 10:8 Hopper.

The Fimbriated forms of -sheaths, -shields, -wafers, -urchins, -pluses, -timeses, -equals, and -abstracts originally had their own suffixes, but I have now replaced these with the same use of Fimbriated as with their components.

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By Charles Gilman.
Web page created: 2008-11-01. Web page last updated: 2016-05-31﻿