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Man and Beast 08: Diverse DirectionsPieces in the articles numbered 1, 2, 4, and 6 in the "See Also" section below are radial, that is, they pass through the centre of any intermediate cell or miss its interior entirely. Those in the articles numbered 3, 5, and 7 are oblique, that is, they pass through the interior of cells while missing their centre. This article's pieces combine both kinds of move. None of these pieces are available on Pentagonal boards.
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.
PiecesThe archetypal such pieces are the MARSHAL, combining Rook and Knight, and the CARDINAL, combining Bishop and Knight. The radial components are usually the stronger, the Cardinal's due to being used on large boards which make Bishops stronger than Knights. Their first recorded use is under different names in the Sicilian Carrera's Chess, soon after the introduction of the modern Bishop and Queen. As the Queen was a Rook+Bishop compound, it was to Carrera an obvious extension to add one each of the other compounds of first-rank pieces. They next appeared under yet other names in two historic forms of British Chess, one in Duke of Rutland's Chess and both in Bird's Chess. Variants of other nationalities have used the pair since but as a British inventor I continue the tradition of their use in variants such as Magna Carta Chess, where the modern names are especially apt. I generally use these names, but accept Marshal alongside its alternative of Chancellor in university-themed variants. Rook+Camel=CANVASSER means one going from house to house (though rarely as grand a house as Rooks represent!) but carries a suggestion of packing tents onto a camel! Bishop+Camel=CALIPH is a title from a religion popular in camels' homelands. The pair appear with the Marshal and Cardinal in my Ecumenical Chess. The ACE or AMAZON combines Rook, Bishop, and Knight moves and often accompanies the three twofold compounds. Ace, the name used in Cardmate, goes well with King and Queen for players of card as well as board games. For Queen+Camel, ACME shares Ace's connotations of high quality, but has the m of Camel. Here are the movement diagrams for the six:
Names can be extrapolated to oblique components other than Knight. Again where the first vowel of such a name is an I it is short, and where a Y long, to distinguish the two. The Mar- of Marshal comes from mare, a horse, so substituting the first three letters of other colourswitching leapers gives Rook+Zebra=ZEBSHAL, Rook+Giraffe=GIRSHAL, Rook+Antelope=ANTSHAL. The Ca- of Cardinal/Canvasser/Caliph, recognisable to those familiar with my oblique-piece articles, gives Bishop+Zebra=ZERDINAL, Bishop+Giraffe=GIRDINAL, Bishop+Antelope=NARDINAL. Rook+Zemel is the Buddhist-sounding ZENVASSER (5:1 leaper), Bishop+Gimel the author-suggesting GILIPH (5:3 leaper), and Bishop+Bittern a highly appropriate BIRDINAL! The reversed letters in Ace give Queen+Zebra=EZE, Queen+Zemel=EZME, Queen+Giraffe=IGE, Queen+Antelope=ANE. An accidental link with Primate (Bishop+Wazir) occurs with Queen+Parson=APE! They can be further extrapolated to 3d components. Two-evens oblique components follow the Knight pattern with the 2:2:1 Ninja generating NINSHAL/NIRDINAL/INE, the 3:2:2 Fencer FENSHAL/FERDINAL/EFE, and the 4:2:1 Overscore OVESHAL/VORDINAL/OVE. Two-odds ones follow the Camel pattern with the 2:1:1 Sexton generating SENVASSER/SELIPH/ESME (the last my mother's middle name), the 3:2:1 Fortnight FONVASSER/FOLIPH/OFME, and the 4:1:1 Nimel NINVASSER/NILIPH/INME. As three-odds leapers lack 2d counterparts I start with 3:1:1 Elf compounds, using Elf's first vowel and consonant as the previous article's Lemming does. For Rook+Elf I go for LEASEHOLDER as someone in relation to their residence, for Bishop+Elf LEVITE as a rank in the historic Jewish priesthood, and for Queen+Elf ELUDER as one dodging capture. This gives 3:3:1 Underscore compounds NUASEHOLDER/NUVITE/UNUDER. The radial component too can have three coordinates. Unicorn+Knight=CAVALCADE from its two kinds of horsiness, as used in my Bipolar variants. Likewise Unicorn+Camel=CAFILA means a caravan in the ancient sense, free of modern structural connotations. These generate ZEVALCADE, GIVALCADE, the nautical-sounding NAVALCADE, NIVALCADE, FEVALCADE, ZEFILA, SEFILA, FOFILA. As Unicorn+Elf has mythical creatures as components a third such creature is LEPRECHAUN, resulting in Unicorn+Underscore=NUPRECHAUN. Treating the Y of the 4:3:2 Rytas as a vowel gives Bishop+Rytas=RYRDINAL, Queen+Rytas=YRE, and Unicorn+Rytas=RYVALCADE.
For a pair of duals or semi-duals as oblique components I start with Gnu compounds, using the reversed letter pair of the Ace/Acme group. Rook+Gnu=ACROPOLIS, after a lofty stronghold. Bishop+Gnu=ACTOR, which like MAB 06's Clown and Buffoon draws on the Bishop as Fool with a performer. It is worth noting that surnames such as Abbot, Bishop, Duke, King, Pope, and Prince originate in actors typecast in such parts. Queen+Gnu=ACTRESS mirrors the femininity of its radial component. These three appear along with the Ecumenical foursome in my Overkill Ecumenical Chess. Unicorn+Gnu=ACTIVIST draws on the subversive names of MAB 01's Unicorn compounds the Besieger, Heretic, and Usurper. The same radial pieces' compounds with the Zebu substitute EZ-, with the Guru IG-, with the Anu AN-, with the Nintu IN-, with the Lefanu EL-, with the Feu EF-, et cetera. Here are the movement diagrams for Acropolis, Actor, and Actress:
For MAB 07's formula compounds Canoe (Knight+Sexton+Ninja) and Caique (Camel+Elf+Underscore) as oblique components I use the initials of the FO Helm and Hump. Rook compounds with Canoe/Caique I name after buildings: HOTEL and HOSTEL. For Bishop compounds I echo the Rook-compound pairing while drawing on the Bishop as runner in mid-Europe, with HURTLER and HUSTLER. Queen compounds I name as strong-willed women: HARRIDAN and HOYDEN. For Unicorn compounds I draw on MAB 19's Unicorn+Heffalump=Herald with HARBINGER and HOLLERER. Rook/Bishop/Queen/Unicorn compounds with the Zenoe substitute the S of Stripe giving SOTEL/SURTLER/SARRIDAN/SARBINGER, with the Ginoe the B of Blotch giving BOTEL/BURTLER/BARRIDAN/BARBINGER, with the Zeique the S of Sump giving SOSTEL/SUSTLER/SOYDEN/SOLLERER, with the Sanoe the C of Vine giving VOTEL/VURTLER/VARRIDAN/VARBINGER, with the Giique the B of Bump giving BOSTEL/BUSTLER/BOYDEN/BOLLERER, et cetera. Rook+Fanoe is notable as being a MOTEL. For compounds with the Nanoe I use third names for lesser items of the same kind starting with H: HOMESTEAD/HIKER/HENPECKER/HARANGUER. For those with the Naique I look to the still lesser HOVEL/HOBO/HAG/HECKLER.
The Gazelle and Bison are notable in the square geometry as the compounds with, respectively, its two shortest, and its two 3rd-perimeter, colourswitching oblique leaps. For this reason I have named their compounds with radial pieces, and ones that echo both names. Rook compounds have bird names starting with R, and Bishop ones religiuos names starting with B. For Queen compounds I was stuck for names starting with Q, but eventually I recalled a suggestion for another of this page's piece and noticed that it was associated with a female character and, in some transliterations, began with the English female-specific pronoun. I therefore selected that and another such name. The full list of Rook/Bishop/Queen compounds with the Gazelle are RAZORBILL/BASILICA/SHEHEREZADE, and with the Bison ROBIN/BIBLICIST/SHEBA. In 3d, their Oberon compounds are TITANIA/IAPETUS/RHEA. The first forms a pair with Oberon both as character and as moon of Uranus, and the other two are the similar-sized moons of Saturn, in both cases the moon with the male name being fuether from its worls and slightly smaller than the one with the female name.
So far this page's pieces combine a long-range radial piece and a short-range (for its direction) oblique one. For vice versa, or both long-range, or both short-range, suffixes can be added to the first five letters of the basic names - or to the whole names of the short-named Queen compounds. I suggest -RIDER where both are long-range, i.e. both riders themselves; -ROVER for swapping the ranges over; and -LANDER for both short-range to make Wazir+Knight the punning MARSHLANDER. Other examples are Rook+Nightrider=MARSHRIDER, Queen+Nightrider=ACERIDER, Rook+Camelrider=CANVARIDER, Bishop+Zebrarider=ZERDIRIDER, Queen+Sextorider=ESMERIDER, Rook+Gnurider=ACROPRIDER, Wazir+Nightrider=MARSHROVER, Ferz+Nightrider=CARDIROVER, Prince+Camelrider=ACMEROVER, Ferz+Zeburider=EZTORRIDER, Ferz+Knight=CARDILANDER, Wazir+Camel=CANVALANDER, Wazir+Ninja=NINSHLANDER, Viceroy+Sexton=SEFILLANDER Prince+Elf=ELUDELANDER, Viceroy+Guru=IGTIVLANDER, et cetera. Some riders and rovers require very big boards, but the likes of the ZENVALANDER are still meaningful on an 8Â² board, and the NIVALLANDER on a 6Â³ one. Adding an oblique move to the General instead of the Wazir, or the King instead of the Prince gives the suffix -RULER, thus General+Knight=MARSHRULER and King+Knight=ACERULER. The Acerider and Aceruler are the Frolov Octagonal analogues to the Queen and King. There are suitable images for the Marsh-, Cardi-, Canva-, Calip-, Zebsh-, Zerdi-, Girsh-, and Girdi-landers and here are the movement diagrams:
On rectilinear boards all -liphs have the Bishop's binding and all -prechauns the Unicorn's. All -vites and -filas are unbound just as Bishop+Unicorn is unbound. Likewise their -riders, -landers, and -rangers in all cases. All -shlanders, -vallanders, -aselanders, and -prelanders are colourswitching. On hex-prism boards few pieces are bound or, except for -liplanders, switching. Compounds becoming switching when Averse to one in three columns include the Cardilander and Girdilander.
On Pentagonal-prism boards only Rook and single-step compounds with n:1:0 and n:1:1 leapers are available - no -riders or -rovers.
As the shortest radial distances are so very short, the next-shortest are also of note, as subordinate to the oblique move. The KANGAROO of Timothy Newton's Outback Chess is a Knight+Elephant compound. Given that Knight itself starts with K, the equivalence of Ka- to Ca- is clear. Knight+Dabbaba suits CARPENTER as Knights require the most craftsmanship in turned Staunton FIDE sets and many kinds of horse (rocking, hobby, dandy) and war engine have been wooden. If Homer is to be believed at least one work of carpentry was both! Lewis Carroll refers to both, the "Kangaroo that ground a coffee mill" in the Gardener's Song and the Carpenter alongside the Walrus. Knight+Trebuchet, Knight+Tripper, Knight+Eunuch, and Knight+Zombie are CATAPULT, CHAPERONE, CAPARISONER, and CANNIBAL - a trebuchet-like weapon, a gallant companion on a trip, a servant equipping horses, and what many zombies in recent films are. For compounds with the Camel (and sharing its binding) Camel+Dabbaba, Camel+Elephant, Camel+Tripper, and Camel+Eunuch are CASBAH, CARIBOU (following the beast+beast=beast rule), CAMPER, and CANTOR (some historic eunuchs being lead singers). The Carpenter, Caribou, and Chaperone can triangulate by two oblique and one radial move. The Camper is colourswitching in 2d but not on cubic boards. Nearlydouble Chess and its offshoots use the Catapult, and some of the latter the Camper. Here are the movement diagrams for Kangaroo, Carpenter, Catapult, Chaperone, Casbah, and Caribou:
For compounds with the Elf (and sharing its binding) Elf+Dabbaba, Elf+Elephant, Elf+Eunuch, and Elf+Zombie are LEGIONARY, LECHWE, LEGENDIST, and the rankswitching LEGBA - a kind of soldier, another African ungulate, a teller of tales about e.g. Elves, and a Voodoo spirit. Some compounds of a non-coprime piece and a differently-bound piece are unbound, and I follow the convention of the MAB 06 Frog, Toad, et cetera with ampbibian names. These include Camel+Trebuchet=CANETOAD, Camel+Zombie=CAECILIAN, Elf+Trebuchet=LEIOPELMA, and Elf+Tripper=LEPTODACTYL. The Leiopelma is, unusually for amphibians, colourswitching. Usual extrapolations inherit bindings and switchings but not triangulation including Sexton compounds SESBAH/SERIBOU/SENTOR/SENETOAD/SEMPER/SEECILIAN, Ninja ones NIRPENTER/NINGAROO/NIPARISONNER/NITAPULT/NHIPERONE/NINNIBAL, Zebra ones ZERPENTER/ZENGAROO/ZEPARISONNER/ZETAPULT/ZHEPERONE/ZENNIBAL, Fortnight ones FOSBAH/FORIBOU/FONTOR/FONETOAD/FOMPER/FOECILIAN, Underscore ones NUGIONARY/NUCHWE/NUGENDIST/NUIOPELMA/NUPTODACTYL/NUGBA, Overscore ones VORPENTER/VONGAROO/VOPARISONNER/VOTAPULT/VHOPERONE/VONNIBAL, et cetera. Zengaroo sounds suitably Buddhist for use in a combined Chinese+Korean variant! Nimel+Trebuchet=NINETOAD is a rarity as a name starting with Nine but nothing to do with the number. Leaping is the default for all these, with stepping alternatives as regards the radial component.
As MAB 06 documents many compounds of multiple pairs of radial duals - Prince+Alibaba=Pasha, Prince+Trilby=Pitcher, Prince+Alibaba+Trilby=Liondog - I add compounds mixing pairs of radial and of oblique ones. Thus Gnu+Alibaba=ACADEMIC, Gnu+Trilby=ACHATES. Achates means another kind of gallant companion, after a character from the Trojan War, and also includes the letters hat in reference to its Trilby component. The usual extrapolations apply so that for example Zebu+Alibaba=EZADEMIC and Zebu+Trilby=EZHATES. Likewise Guru compounds start with Ig-, Nintu compounds with In- , et cetera. Nearlydouble Wildebeest and Fragnurasian Qi use the Catapult, Camper, and Achates.
Again -rider and -rover apply to long-range oblique moves, but as the default is pure short-range a suffix is needed where only the radial is long-range. Indeed two are, one for any even number of steps, another for any strictly exceeding one. Following the rule from MAB 06: The Heavy Brigade for part-coprime all-radial compounds where Waffle=Wazir+Elephant extends to Wafflrider=Rook+Elephrider, Wafflbante=Wazir+Elephrider, Wafflon=Wazir+Picket gives Knight+Dabbarider=CARPEBANTE and Knight+Pocket=CARPEON. For a second all-long-range suffix also required, -DIEM makes Nightrider+Pocket pun on CARPEDIEM (Latin for "sieze the day") as distinct from Nightrider+Dabbarider=CARPERIDER. The same suffixes apply to Kanga-, Capar-, Casba-, Carib-, Canto-, Zerpe-, Zesba-, Separ-, Ninga-, Legio-, Level-, Legen- et cetera. For compounds with thrice-coprime radial pieces note, for example, Knight+Treburider=CATAPTRANTE. Again radial components can have different levels of leaping/stepping.
Conversely, odd-only radial pieces can also have compounds with oblique pieces. Panda+Knight is essentially a Marshal restricted (in 2d) to be colourswitching, so this piece I term a MARSHSWITCHER, and its extension Panda+Nightrider MARSHSWIPER. The same suffixes for Canva-, Zebsh-, Senva-, Ninsh-, Lease- &c also indicate a Panda component; for Cardi-, Calip-, Zerdi-, Selip-, Nirdi-, Levit- &c a Bear component; and for Caval-, Cafil-, Zeval-, Sefil-, Nival-, Lepre- &c a Raccoon component.
Pieces whose oblique component is non-coprime include Rook+Charolais=CABRIOLET and Rook+Crane=CABOOSE after vehicles (the Rook being historically a chariot), and Bishop+Charolais=CALVINIST and Bishop+Crane=CARMELITE after western Christian movements.
Following discussions about piece names in Daniil Frolov's Korean Carrera I acknowledged that pieces with Hopping radial components needed distinct names as simply suffixing "hopper" does not make it clear that the oblique component is not also Hopping. As ever I take the Knight/Camel/Elf compounds as the blueprint for extrapolation. Square-board ones I name after either experienced warriors of unspecified rank - Cannon+Knight=MARKSMAN, Arrow+Knight=CAREERIST, Arrow+Camel=CAMPAIGNER - or financial workers involved in metaphorically "firing" employees or even "gunning for" redundancies - Cannon+Camel=CASHIER, Tank+Knight=ACCOUNTANT, Tank+Camel=ACTUARY. In the armed forces cashiering actually means a form of dismissal. These are extrapolated in the usual way so that Cannon/Arrow/Tank compounds with the Zebra are ZEBKSMAN/ZEREERIST/EZCOUNTANT, with the Giraffe GIRKSMAN/GIREERIST/IGCOUNTANT, et cetera. Elf compounds I name ad hoc. Cannon+Elf=LEGATE, Arrow+Elf=LEISTER (a kind of spear), Tank+Elf=ELIMINATOR (one in the act of dismissing another). Sling compounds I name after old nationalities of the Near East, where Slings were much used historically: CARIAN/CAPPADOCIAN/LEBANESE. My dual-based 3d variant Ecumenical Eurasian Ninjachess has a Marksman, Cashier, Careerist, and Campaigner and their Ninja/Nimel analogues the NINKSMAN, NISHIER, NIREERIST, and NIMPAIGNER. Occasionally extrapolation gives a real word, as in Tank+Sexton=ESTUARY. Here are the Marksman and Careerist piece imges, as used in Overyang and Xiangaroo, and the Accountant in similar vein:
To Pentagonal-prism boards this section adds only Wazir/Ferz/Prince/Viceroy/Rook/Dabbaba/Dabbarider/Pocket/Panda/Cannon compounds with n:1:0 and n:1:1 leapers. Again there are no -riders or -rovers.
Finally there are "formula" compounds. Here m and n are any number between 0 and the largest number in the formula, inclusive. The inclusivity distinguishes them from the purely oblique formula compounds of MAB 07: When Beasts Collide. See that and MAB 06 for the more obscure component compounds. Thus Knight+Alibaba=SQUIRREL is a 2:n leaper. Extrapolating to a cubic board gives a 2:m:n CUBIRREL expressible as Squirrel+Sexton+Ninja+Eunuch or Canoe+Alibuck, and a 2:2:n FRAIRREL=Ninja+Elk (from the frame of a cube). For a 3:n leaper Bison+Trilby=BEAVER, a larger rodent featuring in Lewis Carroll's Hunting of the Snark and, as a bonus, a piece of armour (the part of a helmet covering the chin). This extrapolates to 3d as a 3:m:n TREAVER=Beaver+UNEAVER where Uneaver=Unison+Zombie. Finally I suggest the 4:n MARA=Gleaner+Colby after a more obscure large rodent, and the 5:n CAPYBARA=Corsair+Quilby after the largest rodent of all. As the radial component is non-coprime (but note that so is the Mara's Charolais one) other extensions use the same suffixes as the Carpenter except that some substitute -trante et cetera for -bante. For example SQUIRRIDER=Nightrider+Alibarider, SQUIRBANTE=Knight+Alibarider, BEAVETRANTE=Bison+Trilbrider, BEAVEROVER=Bisonrider+Trilby, MARABANTE=Giselle+Charorider+Colby, MARAQUADRANTE=Giselle+Charolais+Colbyrider, MARADIEM=Giselrider+Charoon+Colbyon. Here is the movement diagram for the Squirrel:
For diamond-pattern formula compounds I prefix END- to the compound without the orthogonal move, of which only Zemel+Charolais+Tripper is not yet covered so I name that TRAMPLER. Those with odd sums of coordinates are colourswitching - n:5-n ENDGAMEWARDEN=Gamewarden+Quibbler (the pun inspiring the prefix!) and n:7-n ENDSWAN=Swan+Settler - and those with even sums colourbound - n:4-n ENDCARIBOU=Caribou+Cobbler, the Squirrel's colourbound dual, and 6:n-6 ENDTRAMPLER=Trampler+Bitrebuchet, the Beaver's. For the colourswitching ones' square-pattern colourbound (and rankswitching) counterparts I prefix DIA- for diagonal, making Cogamewarden+Quitter the 5:5-2n DIACOGAMEWARDEN. In 3d diamonds can become octahedra: OCTKNIGHT=Catapult+Viceroy, OCTCARIBOU=Endcaribou+Sexton, OCTGAMEWARDEN=Endgamewarden+Ninja+Elf, OCTTRAMPLER=Endtrampler+Fortnight+Nimel+Eunuch, OCTSWAN=Endswan+Fencer+Underscore+Overscore.
To Pentagonal-prism boards this section adds the Octknight.
NotesPieces with a radial and an oblique component, one or both forward-only or Curved or Crooked or hex-specific, are covered in MAB 19: The Vice Squad.
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By Charles Gilman.
Web page created: 2008-01-30. Web page last updated: 2013-12-27