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Man and Beast 09: Mighty Like a Rose
IntroductionLong-range pieces in the first 8 articles in the "See also" section below follow Straight paths: having taken a step or leap they repeat it in the same direction. This article's pieces turn on one or more intermediate cells. It is something of a meta-article of which Peter Aronson, Ralph Betza, and JÃ¶rg Knappen cover subsets. They are Curved (repeating left or right turns but not mixing them), Crooked (alternating left and right turns), or Bent (turning only on a single intermediate cell). Another division is between using one kind of direction and two alternating ones. The former can also, like Straight linepieces, make the single short-range move, and can be identified as the Straight piece prefixed with the angle(s) and turn type. None of the pieces considered here are available on a pentagonal board or, unless specified, meaningfully on a pentagonal-prism one.
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 name of the best-known Curved piece, the ROSE, reflects its move, the flower's heraldic use, mention in Lewis Carroll's Alice books, and as a Knight extension the opera Der Rosenkavalier. A Curved Nightrider, it makes one or more Knight leaps but turns at each intermediate cell. It never mixes left and right turns in one move, but what does change within a move is the angle turned, approximating to 53Â° when reflecting off an orthogonal but to 37Â° when reflecting off a diagonal. Theoretically it can start and end a move on the same cell, but some games bar such a null move. Here is the movement diagram for the Rose, with numbers marking the number of Knight leaps taken to reach each square:
Extrapolating to other 2d oblique directions I noted how the H of horse is often dropped in speech, and the simplest dictionaries illustrate pronunciation of a long O as oh. This link between Knights as (h)orses and ro(h)ses inspired calling the Curved Camelrider MACEL and the Curved Zebrarider BEZRA. The likeness to Betza is an added bonus! The Macel alternates 37Â° and 53Â° turns but the relation to orthogonals and diagonals reverses. The Bezra turns 67Â° off orthogonals and 23Â° off diagonals. Others' O/D angles I show in brackets. The name can be seen as reversing the first three letters or swapping the first two consonants. Both give RIGAFFE (28Â°/62Â°), MEZEL (23Â°/67Â°), TASYR (44Â°/46Â°), MIGEL (62Â°/28Â°), TIBTERN (14Â°/76Â°), CERTOR (77Â°/13Â°), RAPSON (80Â°/10Â°), RUCATE (81Â°/9Â°). The last three reflect little off diagonals but sharply off orthogonals. Where they differ I use whichever sounds better: ATNELOPE (74Â°/16Â°), TSORK (32Â°/58Â°), ARGONOME (64Â°/26Â°), ABLATROSS (25Â°/65Â°) but ALFMINGO (19Â°/71Â°), XO (59Â°/31Â°). The Alfmingo and Tibtern reflect little off orthogonals but sharply off diagonals. A Curved Mamelrider I term AMARYLLIS. Their compounds I similarly name - UNG, ZAGELLE, SIBON, FUBFALO, MAGEWARDEN, BOCISON, BEZU, VOHERCRAFT, JAHJ, TAB. Where non-coprime oblique piece names insert an H or R between direction letters, removing that letter with no reversal gives CAROLAIS, CANE, CAMOIS, ZEROLAIS, GIROLAIS, NAROLAIS, ZENE, and ZEMOIS. These and the more straightforward LACTRAP and SACSOWARY require Really Big Boards.
Extrapolating to radial directions looks awkward on rectilinear boards as the angles reach 0Â°/90Â°, but hex boards have an all-60Â° Curved Rook and Unicorn. As coprime radial pieces have special names I named these FINCH and RABBI in my hex variant Anglojewish Chess. Their compound is a COHEN or KOHEN, after a higher rank than the previous page's Levite in the historic Jewish priesthood. On hex-prism boards the Finch and Cohen can also move one step at right angles to the hex plane like a regular Wazir, likewise the BADBABA (Curved Dabbarider) 2 steps, ERTBUCHET 3, and BOCBLER 4. Compounds with a non-coprime element follow the usual rule: Finch+Badbaba=ZAWBABA, Rabbi+Badbaba=CIVBABA, Finch+NUEUCH=ZAWZOCK, Rabbi+Nueuch=NIVNOCK, Badbaba+Nueuch=BYDBUK, Finch+Ertbuchet=TAWCHER, Rabbi+Ertbuchet=LUBLFROG, Badbaba+Ertbuchet=AOTD, Nueuch+Ertbuchet=ETF, Finch+MOZBIE=RAWMER, Rabbi+Mozbie=CIVTOR, Badbaba+Mozbie=ZADZLER, Nueuch+Mozbie=OOZKEEPER, Ertbuchet+Mozbie=ERTBIZOND, Finch+Bocbler=ROCDWAINER. Cubic boards have a dual of the Finch, a Curved Bishop whose path might for example comprise +1:+1:0, +1:0:+1, 0:-1:+1, -1:-1:0, -1:0:-1, and 0:+1:-1 steps. Being intermediate between Bishop and Rabbi it suits the transitional name APOSTLE. Indeed all m+n:m:n leapers have cubic 60Â° Curved riders - the XESTON, FLAIL, ROFTNIGHT, IRTPPER, SENE, ABREZ, MOCMUTER, TOVARY, EDNOWER, NABDICOOT, and MEHEL. The special case of the Curved Sustainer I resort to turning "inside out" to USUTAINER. A sample sequence of steps is +(m+n):+m:+n, +n:+(m+n):-m, -m:n:-(m+n), -(m+n):-m:-n, -n:-(m+n):+m, +m:-n:+(m+n). Cpmpounds include Apostle+Flail=AEFRFUL, Apostle+Irtpper=TEFCHER, Flail+Irtpper=IRTFLE. As the Rabbi and Rose cannot occur on the same 2d board and I do not expect them to share a 3d one often, I use the same image. Here are the movement diagrams for the Finch, Rabbi, and Cohen:
Radial+oblique compounds are named the same way. On hex 3d boards Finch+Rose=RAMSHAL, Rabbi+Rose=VACALCADE, Finch+Macel=NACVASSER, Rabbi+Macel=FACILA, Finch+Bezra=BEZSHAL, Rose+Badbaba=RACPENTER. On the cubic board Apostle+Rose=RACDINAL, Apostle+Xeston=LESIPH, Apostle+Macel=LACIPH. "Inside-out" namings include Finch+Manel=ANAVASSER, Atnelope+Flail=ANAGAROO, Rabbi+Mafel=AFAILA, Apostle+Certor=EREDINAL, Certor+Badbaba=EREPENTER.
Crooked pieces alternate left and right turns - and/or up and down on 3d boards - but at constant angles by which I distinguish them. Moves comprising even numbers of leaps average out to a given type of direction, the Even Move Direction (EMD).
Symmetric square-board pieces have 90Â° Crooked riders, whose EMD is the starting direction's dual. Best known is the BOYSCOUT or Crooked Bishop, EMD orthogonal, followed by the GIRLSCOUT or Crooked Rook, EMD standard diagonal. My 4 Linepiece Fusion adds their compound the DOUBLESCOUT. I extend the -scout theme to LONGRANGESCOUT for the 70Â° (EMD standard diagonal), and SHORTRANGECOUT for the 110Â° (EMD orthogonal), Crooked Unicorn and RANGESCOUT for their compound. For other 90Â° Crooked pieces, replacing -rider with -DUELLER puns on the EMD's duality and a dueller being a fighter. Thus the NIGHTDUELLER's EMD is Camelwise, the CAMELDUELLER's Knightwise, the DABBADUELLER's and TREBUDUELLER's diagonal, the ELEPHDUELLER's and TRIPPDUELLER's orthogonal, the ZEBRADUELLER's Zemelwise, the GIRAFDUELLER's Gimelwise, et cetera. Cubic boards add a NINJADUELLER with both Nimelwise and orthogonal EMDs. Compounds include WAFFLDUELLER, FEZBADUELLER, FROGDUELLER, GNUDUELLER, GAZELDUELLER, BISONDUELLER, BUFFADUELLER. The likes of WAZBADUELLER, TOADDUELLER, FEARFDUELLER, and FETCHDUELLER correspond to no compound Straight linepiece. Radial+oblique compounds include the likes of Boyscout+Nightdueller=CARDIDUELLER, Girlscout+Cameldueller=CANVADUELLER. Here are the movement diagrams for the Girlscout, Boyscout, Doublescout, and Nightdueller:
Other Crooked square-board oblique linepieces occur in fours. Angles x and 180-x give an orthogonal EMD and 90-x and 90+x a diagonal EMD, x and 90-x being the Curved piece's alternating angles. These again use -rider substitutes: the orthogonal-EMD -FLYER (alluding to the Rook), diagonal-EMD -SIDLER, and -LADY (alluding to the Queen) for all four. Each of the three can be prefixed LONG- for just the component turning less and SHORT- for just that turning more. Rounding turns to the nearest degree this gives a 53Â° LONGNIGHTFLYER, 127Â° SHORTNIGHTFLYER, 37Â° LONGNIGHTSIDLER, 143Â° SHORTNIGHTSIDLER, 53Â° and 127Â° NIGHTFLYER, 53Â° and 37Â° LONGNIGHTLADY, 127Â° and 143Â° SHORTNIGHTLADY, 37Â° and 143Â° NIGHTSIDLER, and all-four NIGHTLADY. For -night-'s 53/127/37/143 -CAMEL- has 37/143/53/127 (a different order, note), -ZEBRA- 67/113/23/157, -GIRAF- 28/152/62/118, and so on. As just one example of many multi-oblique compounds, a LONGGNUFLYER would turn 53Â° between Knight leaps but 37Â° between Camel leaps, never mixing the two within one move. In September 2014 Carlos Cetina ranked the relative strengths of Nightriders, in the descending order: Shortnightsidler, Shortnightflyer, Nightdueller, Rose, Longnightsidler, Straight Nightrider, Longnightflyer. Here are the movement diagrams for the Longnightflyer, Shortnightflyer, and their compound, with the plain blue circles indicating the squares reachable in 2 Knight leaps by the Long-, and 4 by the Short-, -nightflyer:
Cubic boards give the Longnightsidler a second EMD, Nimelwise. For other coordinates m:n (m larger than n) the 2m:n:n EMD has a different angle, and the 0:n:n EMD 180 minus that angle. I suggest the suffix -angler, e.g. the 26Â° LONGCAMELANGLER and 154Â° SHORTCAMELANGLER. For EMDs of m:m:2n and m:m:0 I suggest -cuber, for example the 78Â° LONGNIGHTCUBER, 102Â° SHORTNIGHTCUBER, 84Â° LONGCAMELCUBER, and 96Â° SHORTCAMELCUBER. Finally for EMDs of m+n:m:n and m:n:m-n I suggest -turner, for example the 66Â° LONGNIGHTTURNER, 114Â° SHORTNIGHTTURNER, 73Â° LONGCAMELTURNER, and 107Â° SHORTCAMELTURNER. Note the unconnected EMDs of these three kinds of rider of dual pieces. As in 2d, Long- plus Short- is unprefixed and the sum of two same-suffixed pieces is the short-range compound so suffixed. Special cases are Nightsidler+Camelangler=GNUANGLER, Nightsidler+Zebraangler=GAZELANGLER et cetera and their prefixed components. Crooked triaxial pieces' angles do not add to 180Â° as the 71Â°/132Â° SEXTOFLYER, 109Â°/146Â° SEXTOSIDLER, 96Â°/141Â° NINJAFLYER, 39Â°/153Â° NINJASIDLER, 50Â°/145Â° ELFFLYER, and 63Â°/130Â° ELFSIDLER show. 3 distinct coordinates give three components, with -MID- inserted for the middle one: a 73Â°/115Â°/149Â° FORTNFLYER and 38Â°/82Â°/158Â° FORTNSIDLER. Non-coprime flyers, sidlers, ladies, anglers, cubers, and turners (Charo-, Crane-, Chamo-, Zhero- et cetera) inherit the corresponding coprime piece's angles.
Hex boards have 60Â° Crooked Rooks (EMD ND) and Unicorns (EMD orthogonal), and cubic ones 60Â° Crooked Bishops (EMD Sextonwise) and Sextoriders (EMD SD). They also have 120Â° ones, whose EMDs are their own Straight versions' directions. For these I extrapolate from -scout names to GIRLHEXER for the Rooks, BOYHEXER for the Bishops, and RANGEHEXER for the Unicorns, all prefixed with LONG- for just 60Â° and SHORT- for just 120Â°. Likewise the non-coprime DABBAHEXER, TREBUHEXER, EUNUCHEXER. On hex-prism boards the Girlhexer can also move one step at right angles to the hex plane like a regular Wazir, likewise the Dabbahexer 2 steps. The Asteryx Chess Bishop analogue is a Longgirlhexer, while John Smith's Neptune names it even more exotically. Cubic-cell m+n:m:n leapers also have 60Â° and 120Â° Crooked riders - the similarly prefixed SEXTOHEXER, ELEPHHEXER, FORTNHEXER, TRIPPHEXER, SRENEHEXER, ARBEZHEXER, SUSTAHEXER, and VOTARHEXER. Compounds inherit the suffix, and prefixes if any, giving hex boards (Long, Short, and unprefixed) DUKEHEXERS, WAZBAHEXERS, VICBAHEXERS, WAZZOHEXERS, DYBBUHEXERS, VINNOHEXERS et cetera and cubic ones SELIPHEXERS, FEARFHEXERS, SERIBHEXERS, FOLIPHEXERS et cetera. As cubic boards have the Boyscout itself it has a compound with [Long-/Short-]Boyhexer, the [LONG-/SHORT-]BOYSIXER, after the boy leading a "six" of cub scouts. To have both Girlscout and Girlhexer requires a 3d hex board, giving the compounds [LONG-/SHORT-]GIRLSIXER. Likewise for non-coprime Crooked radial pieces. The AVERSE LONGGIRLHEXER is slightly odd in that a board where all pieces are Averse to cells of the same colour effectively compounds it with the Unicorn - although non-Averse pieces can block it on both routes. To create a genuine triangular feeling requires a piece which cannot even pass through the cells to which it is Averse is required. Such pieces I term PHOBIC, thus the PHOBIC LONGGIRLHEXER.
The only pieces of this group available on a pentagonal-prism board are the Boyscout, Shortrangescout, Long n:1 flyers - the Longnightflyer, Longcamelflyer, Longgirafflyer, Longzemelflyer et cetera - and Long n:1:1 flyers - the Longsextonflyer, Longelfflyer, Longnimelflyer et cetera. Even these can move only in a primarily vertical direction, never more than one column at a time.
Pieces alternating stages of different Straight moves spring from Xiang Qi's MAO or stepping Knight: this always makes a Wazir move, turns 45Â°, and makes a Ferz move. Though an error by Dawson, the name Mao could be interpreted as Japanese for "Horse King" - reaching Knight destinations by means of two King steps! It has stuck to the point of extrapolation to the MOA which makes the Ferz move first. Here are the movement diagrams for the Mao and Moa, with the pass-through squares marked ina different colour to the destination ones:
Two stepping Nightriders alternate equal numbers of Wazir and Ferz steps, the MAORIDER starting with a Wazir move and ending with a Ferz one and MOARIDER the other way round, and two one more of one than the other, the WAVERER starting and ending (including just) as a Wazir and FEVERER starting and ending (including just) as a Ferz. Peter Aronson adds RHINO - short for RHINOCEROS - family of pieces: the short-range Mao+Wazir and Moa+Ferz and the long-range Maorider+Waverer and Moarider+Feverer. To these I can add similarly prefixed CONTRARHINO pieces (analogous to the Contragrasshopper): Moa+Wazir, Mao+Ferz, Moarider+Waverer, and Maorider+Feverer. Rhino and Contrarhino pieces have a Knightwise EMD. To complete the set Mao+Moa=MOO, Maorider+Moarider=MOORIDER, and I add Waverer+Feverer=UNHORSER for its lack of Knightwise moves. As well as Rhino+Mirror Rhino the DOUBLE RHINO can be seen as Contrarhino+Mirror Contrarhino or Moorider+Unhorser. 45Â° alternators can also be Curved, menign that each move involves wither just clockwise or juswt anticlockwise turns, rather than altrernationg between the two. John Savard's Leaping Bat Chess features a CURVED DOUBLE RHINO. Here are the movement diagrams for the unprefixed Rhino in Crooked and Curved form, then the Mirror Rhino likewise, and finally the Double Rhino likewise:
Gnu leaps too can alternate with 45Â° turns. Such pieces, EMD Antshalwise, I name after the similarly heavy HIPPOPOTAMUS with the same prefixes as Rhino. Extrapolating the -potamus suffix (alternation/EMDs) are the CAMELPOTAMUS (Camel/Charolais, Naliph), ZEBRAPOTAMUS (Zebra/Zemel, Bat), GIRAFPOTAMUS (Giraffe/Gimel, Priestess), ANTELPOTAMUS (Antelope/Namel, Knight+Quail), ZEMELPOTAMUS (Zemel/Zherolais, Cobat) GIMELPOTAMUS (Gimel/Ghirolais, Copriestess), and NINJAPOTAMUS (Ninja/Nimel, Knight). Hippopotamus pieces restricted to moving exactly two leaps I term the MAOSQUARED (Knight then Camel), MOASQUARED (vice versa), and MOOSQUARED (either). Alternating between longer radial leaps I name Ferz/Dabbaba, Wazir/Elephant, Ferz/Trebuchet, Dabbaba/Elephant, Wazir/Tripper, Elephant/Trebuchet, Ferz/Quibbler, Elephant/Cobbler, Wazir/Commuter, Elephant/Quibbler, and Wazir/Quitter alternators ALPACA, QUAGGA, OKAPI, ALDERNEY, SPRINGBOK, TRAGOPAN, FLATTENER, AVOCET, RENDER, STALKER, and PARISHIONER for their Camel, Zebra, Giraffe, Charolais, Antelope, Satyr, Flamingo, Crane, Rector, Stork, and Parson two-leap destinations. Alpaca extrapolates to QUALPACA for Ferz/Cobbler, OKALPACA for Dabbaba/Tripper, SPRILPACA for Ferz/Bitrebuchet, alternators and Alderney to QUALDERNEY for the Dabbaba/Commuter one. Crooked pieces inherit the oblique one's binding or lack thereof. Right-angle turns between different-length orthogonal moves - Wazir/Dabbaba, Wazir/Trebuchet, Dabbaba/Trebuchet, Wazir/Cobbler, Trebuchet/Cobbler, Wazir/Quibbler, Dabbaba/Quibbler, Trebuchet/Quibbler - give the SIDERHINO, SIDEALPACA, SIDEQUAGGA, SIDEOKAPI, SIDESPRINGBOK, SIDEQUALPACA, SIDETRAGOPAN, SIDEOKALPACA. All are unbound. Likewise different-length diagonal moves - Ferz/Elephant, Elephant/Tripper, Ferz/Commuter - give CORNERALPACA, CORNERQUALPACA, and CORNEROKALPACA. All have the Bishop binding. Here are the movement diagrams for the Double Hipppopotamus, Double Alpaca, and Double Quagga, again in Crooked followed by Curved form:
Alternators of all angles can also be Switchback, alternating between steps of a Straight move and one that is itself Crooked. They are termed SHORT-SWITCHBACK if the shorter stages are of the Straight move and LONG-SWITCHBACK if the longer ones are. SWITCHBACK without further qualification is the compound of the two. Thus the Short-Switchback Rhino and Long-Switchback Alpaca have an orthogonal CMD, and the Long-Switchback Rhino and Short-Switchback Alpaca a diagonal one. Curved Alpacas orbits a cell a Knight's move from all cells on its path, likewise Curved Alderneys with Camel leaps, Qualpacas with Zebra leaps, Okalpacas with Giraffe leaps, et cetera. The unbound ones can similarly be seen as orbiting the corner of a square, or in 3d the edge of a cube, a fixed distance from the cells of its path, the square of which is 2Â½ for Curved Rhinos, 6Â½ for Curved Quaggas, 8Â½ for Curved Okapis, et cetera. Here are the movement diargams for the unprefixed Rhino in Long- and Short-switchback form, then the Mirror Rhino likewise, and finally the Double Rhino likewise:
Short- and Long- switchback Rhinos
On cubic boards the 90Â° Wazir/Ferz and Ferz/Viceroy, 55Â° Wazir/Viceroy, and 35Â° Ferz/Viceroy alternators are TAPIR, HYPERRHINO, NAVVY, and THUG for their Unicornwise/Knightwise/Sextonwise/Ninjawise EMDs. All are unbound. The UNHORNER, HYPERUNHORSER, colourswitching EXHUMER, and UNMASKER move only odd numbers of steps. Further pieces (alternation, EMD) share these turning angles. 55Â° has DWARF (Vicbaba, Elf), JOUSTER (Wazzock, Fencer), THULPACA (Bullfrog, Nimel), EXECUTIONER (Viceroy+Cobbler, Exorcist), EXTENDER (Eft, Longplayer), IPAKO (Warmer, Effarig), NUTCRACKER (Viceroy+Quibbler, Nurturer), FIELDJOYSTICK (Dazzler, Fieldmouse), DIETER (Viceroy+Bitrebuchet, Slimmer), NUMCLUB (Wazir+Corpse, Numbat), WOMCLUB (Eunuch+Quitter, Wombat), THUVOCET (Eunuch+Bitrebuchet, Nrine). 35Â° has UNDERLINE (Wilful, Underscore), MENTOR (Fezzock, Lecturer), EXPANDER (Natterjack, Wideplayer), THULDERNEY (Elk, Nhirolais) REDNER (Paddick, Rotcer), DINER (Viceroy+Commuter, Feaster), EXAGGERATOR (Juniper, Expounder), and WAYFARER (Lazarus, Broadwayman). Right-angle turns between an orthogonal and an SD move are a peculiarity of cubic and xyrixa boards including the ANGLENAVVY (Fezbaba, Sexton), ANGLETHUG (Waffle, Ninja), ANGLEDWARF (Frog, Elf), ANGLEJOUSTER (Newt, Fencer), ANGLETHULPACA (Confection, Nimel), ANGLEUNDERLINE (Warper, Underscore), and ANGLEMENTOR (Tribune, Lecturer). 90Â° alternators between an SD and an ND move include the BROWNIE (Wilful, Elf) and FORTIFIER (Fezzock, Fortnight). Thulpacas and Ipakos are unbound, and the rest have the corresponding leaper's binding or lack thereof.
Compounds worth naming include Rhino+Navvy=CHURCHGOER, Rhino+Thug=GANGSTER, and Navvy+Thug=PUCK. These are inspired by MAB 05's Churchwarden, Samurai, and Oberon. Adding in duals the Treasure, Merchant, and Duquelle inspire Navvy+Alpaca=SWAG, Thug+Alpaca=SPIV, and Navvy+Thulpaca=WHOSE (English translation of duquelle) while full duals are Rhino+Thulpaca=COSPIV and Alpaca+Thulpaca=COGANGSTER. Rhino+Alpaca I term ANGORA as any of various animals of Alpaca-like wooliness. This extrapolates to Thug+Thulpaca=THUNGORA, Quagga+Qualpaca=QUANGORA, Okapi+Okalpaca=OKANGORA, and Sprigbok+Sprilpaca=SPRINGORA. For the complete combination of Rhino/Quagga/Okapi/Springbok and their compounds I resort to combining component names. Thus Rhino/Alpaca+Quagga=REQUIRER/ACQUIRER, Rhino/Alpaca+Okapi=RELOCATOR/ALLOCATOR, Quagga/Qualpaca+Okapi=QUOKKA/CLOCKER, Rhino/Alpaca+Springbok=RESPIRATOR/ASPIRATOR, Quagga/Qualpaca+Okapi=QUASIT/CLOSET, and Okapi/Okalpaca+Springbok=OCCASION/OCCLUSION. A quokka is a kind of wallaby, and a quasit is an obscure monster. As usual, pieces prefixed Co- replace bogh components with their duals. Dwarf+Mentor=MEDLEY (a musical term), Jouster+Ipako=JOULE (a unit of energy), and Underline+Nutcracker=SHURIKEN (a ninja weapon) in allusion to MAB 05's Lefanu, Feu, and Nunchaku while Executioner+Exaggerator=EXCEEDER. 60Â° has a rich seam of alternators between standard-diagonal pieces with Curved as well as Crooked forms - Ferz/Elephant, Ferz/Tripper, Elephant/Tripper, Ferz/Commuter, and Ferz/Quitter alternators termed FORTRHINO, AGGAUQ, MAINTAINER, SWEARER, and IMPOSER for their Fortnight/Arbez/Sustainer/Votary/Endower EMDs.
The only pieces of this group available on a pentagonal-prism board are those alternating orthogonal stages with Ferz or Viceroy ones, and even they cannot exceed three stages - two vertical with the Ferz or Viceroy step in between - unless they are Switchback ones with the Straight stages along orthogonals. Rhinos and Navvies can also make a Wazir step, and pieces with a Ferz stage a Ferz step, horizontally.
The best-known Bent piece is named after the flying monster GRYPHON (Classical spelling, also favoured by Lewis Carroll). It is usually defined as moving as a Ferz, turning through 45Â°, and continuing as a Rook. Ralph Betza describes, but does not name, many more Bent Riders. The colourswitching Wazir/45Â°/Bishop piece is often termed AANCA but as the Spanish for Gryphon (monster and piece) this is unsatisfactory, so I use the similar-sounding ANCHORITE, after a kind of religious hermit. Combining the Rook's flying/Bishop's religious/Unicorn's horsy qualities with qualities of destination-sharing 2d and 3d oblique leapers in the format name (name's definition; start/turn/remainder; relevant leapers) gives ZEPHYR (a wind; Elephant/45Â°/Rook; Zebra), LAMA (religious title punning on Llama; Dabbaba/45Â°/Bishop; Camel) SIMURGH (mythical man-headed bird; Viceroy/55Â°/Rook; various human rÃ´les), CELEBRANT (a generalisation of the clergy to modern religions; Viceroy/35Â°/Bishop; various human rÃ´les), FARRIER (uses fire on iron to shoe horses; Wazir/55Â°/Unicorn; Fencer+Effarig=Feu), NAG (a horse but also a didactic person; Ferz/35Â°/Unicorn; Lecturer/Expounder), AVIATOR (flying warrior; Eunuch/55Â°/Rook; Fencer) THEOLOGIAN (authority on religion; Eunuch/35Â°/Bishop; Lecturer/Expounder), PONY (carries lighter loads; Dabbaba/55Â°/Unicorn; Elf/Fieldmouse), PATHFINDER (path goes under horse; Elephant/35Â°/Unicorn; Underscore/Broadwayman). The Celebrant is colourswitching, the Lama and Theologian share the Bishop's binding, and the Pony and Pathfinder share the Unicorn's. On hex boards the Simurgh/Farrier/Aviator/Pony turn 30Â° instead of 55Â°. On hex-prism ones the Celebrant/Nag/Theologian/Pathfinder turn 52Â° instead of 35Â°. Dabbaba, Elephant, and Eunuch stages can theoretically be leaping but stepping will, I suspect, be more usual and is a more logical default. Here are the movement diagrams for the Gryphon and Anchorite o a square-cell board, and the Simurgh and Farrier on a hex one, with the pass-through squares marked in a different colour to the destination ones:
Combining opposite-turn pieces gives Gryphon+Anchorite=GORGON, Zephyr+Lama=FULMAR, Simurgh+Farrier=MECHANIC, Celebrant+Nag=LAYPREACHER, Aviator+Pony=PEGASUS, Theologian+Pathfinder=PILGRIM. Combining those sharing a short move gives Gryphon+Nag=HIPPOGRYPH, Anchorite+Farrier=OSTLER, Zephyr+Pathfinder=TRADEWIND, Lama+Pony=HIGHHORSE, Simurgh+Celebrant=TERMAGANT (demoness ending in -ant), Aviator+Theologian=ASTRONAUT. Prefixing the name of a piece having a single-step short stage with FIMBRIATED, a heraldic term for giving a device on a shield a border of a third colour touching both device and background, adds the corresponding piece with a double-step one. To Gryphon this adds Zephyr, to Anchorite Lama, to Simurgh Aviator, to Celebrant Theologian, to Farrier Pony, to Nag Pathfinder, to Gorgon Fulmar, to Termagant Astronaut, to Chimera Tradewind, to Hippogryph Pegasus, to Ostler Highhorse, and to Laypreacher Pilgrim. For combining two single or double short moves I suffix the straight piece whose move is flanked: Gryphon+Simurgh=ROOKSHEATH, Anchorite+Celebrant=BISHOSHEATH (still colourswitching), Zephyr+Aviator=ROOKSACK, Lama+Theologian=BISHOSACK (preserves Bishop's binding), Farrier+Nag=UNICOSHEATH, Pony+Pathfinder=UNICOSACK (preserves Unicorn's binding). Fimbriating a -sheath adds the -sack. The prefixes QUEEN-, DUCHE-, GOVER-, and EMPRE- represent Rook-+Bisho-, Rook-+Unico-, Bisho-+Unico-, and all three. The compound of all 12 simple Bent pieces is a FIMBRIATED EMPRESHEATH. Here are the movement diagram for the squarecell Gorgon and hex Mechanic:
Prefixing Bent pieces with CONTRA- indicates that the long move comes first, with the word DOUBLE indicates either order, and with LIGHT or HEAVY limits destinations to those with an odd or even long move. Compounds inherit Contra- and Double so that for example CONTRAGRYPHON+CONTRAANCHORITE=CONTRAGORGON. Light and Heavy Gryphons I give the specific names NIGHTINGALE for its Knight and assorted Big Bird destinations and ANGEL for the Anchorite ones' duals (-mel), and for Light and Heavy Anchorites ARCHDEACON for its (among others) Antelope/Parson/Deacon destinations and RECEIVER for its (ditto) Rector/Curate/Verger ones. Names for compounds of a simply-named and Contra-named Bent piece comprise the former's first 5 letters (except for Nag, where they run out) followed by the latter's letters 7 to 11 (likewise for Contranag). Thus the GRYPHANCHO starts on the SD and ends on the orthogonal, and the ANCHOGRYPH vice versa, but may make their turn on the first or last intermediate cell. The GRYPHSIMUR makes a Rook move preceded by a Ferz step
or followed by a Viceroy one but not both and not neither. Pieces can also combine two stages with more diverse pairs of radial moves, such as two long-range ones or one Hopping. These can be described with the two stages hyphenated together followed by MONSTER, so that the Mao is a WAZIR-FERZ MONSTER and the Gryphon a FERZ-ROOK MONSTER. This ties in with Monster Chess, which considers a series of such pieces.
Gryphons and Simurghs are available on a pentagonal-prism board but only with their long stage in a vertical direction.
Crooked odd-move pieces alternate between destinations on two paths of Bent pieces. Names combine the start of the Straight piece and end of the Bent one, where possible alluding to the latter. Square-cell boards have the PROSELYTE, meaning someone changing religion, is a 90Â° Crooked Panda switching Anchorite paths and the BRUEGEL or BRUEGHEL, a 90Â° Crooked Bear switching Angel paths and named after a family of Dutch artists. For Proselyte+Bruegel - a Crooked Harlequin switching Gorgon paths, HALCYON as a synonym for kingfisher conveys a Kinglike combining of orthogonal and diagonal. On hex boards the PLATER, meaning someone covering one metal with another, is a 60Â° Crooked Panda switching Farrier paths and the PLOUGH a 120Â° one switching Simurgh paths. The ROUGH is a 110Â° cubic, or 60Â° hex, Crooked Raccoon, switching Simurgh paths. On cubic boards the REPENTANT is a 70Â° cubic Crooked Raccoon switching Celebrant paths. There are also Curved odd-move pieces. On hex boards the NAPDA, CARCOON, and NAPTALOON differ from the Badbaba, Nueuch, and Bydbuk - and on cubic ones the AEBR from the Flail - in starting halfway along a side of the hexagon. They still end at a corner as usual.
All these pieces have Hopping versions requiring exactly one intervening piece for either all moves (Hoppered or Korean-style), or capturing ones (Canonised or Chinese-style), or noncapturing ones (Beatified). So far I have devised names for Hopping Curved pieces. The 60Â° Curved Cannon, Arrow, and Sling - pieces requiring exactly one intervening piece for certain moves - suit weapon names suggesting curving movement: REVOLVER, MORNINGSTAR, and BOOMERANG. For the compound Revolver+Boomerang I suggest GRENADE, after something sending explosive in all directions. I am unaware of any of these four pieces having yet been used. For the 90Â° Crooked Cannon and Arrow the names GUNWOMAN and GUNMAN combime the Girlscout/Boyscout sex difference with the weaponry theme. The first use of these two pieces, unless I have overlooked some previous use, is in Xiang Qi with Different Armies, with the Korean-style form of the Gunwoman in the Crushing Cannons army and the Chinese-style form of the Gunman in the Diagonal Destroyers one.
NotesDoubly-Bent pieces and pieces mixing Straight/Curved/Crooked/Bent moves share the article MAB 13: Straight and Crooked Moving. The Plough above is at least consistent with some of the latter. The final four articles of this series cover Curved and Crooked (as well as Straight) pieces yet more complex.
As no normal geometry has both Finch and Apostle there is no need to name a pure-Curved Queen, Acerider, Acmerider, et cetera.
In Nachtmahr JÃ¶rg Knappen terms the 90Â° Crooked Nightrider a Quintessence, but extrapolating by substituting other Latin ordinals proved too cumbersome once SOLL exceeded 10 and Nonessence would not distinguish Trebuchet/Ninja moves. The pun inpiring my own use of -dueller is not exactly original. The Blackadder episode Duel and Duality is well known, at least in Britain, but there is a still earlier example of this pun. In Gilbert Keith Chesterton's Father Brown story The Duel of Dr. Hirsch, the man challenged by Dr. Hirsch is very much his dual.
For Curved oblique riders I considered but soon rejected extrapolating from Rose to other plant names. Not only were the names not that obvious in meaning, I could devise relatively few. Amaryllis is a legacy of this.
Originally I termed Fimbriated -sheaths -rounders, but I have now replaced this with the same use of Fimbriated as with their components.
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By Charles Gilman.
Web page created: 2008-02-10. Web page last updated: 2016-05-31