Man and Beast Overview and Glossary

SERIES ACKNOWLEDGMENTS

Contemporaries:
Ezra Bradford and Mark Thompson (Chess variant developer) helped me see the duality between cubic and xyrixa boards, along with other mathematical patterns such as semi-duality on cubic boards.
Julie Rosenfield encouraged me to pursue the Jewish theme for Curved hex pieces (09).
Isis Maitreya pointed out the statues inspiring the Harlequin theme for compounds of odds-only pieces (06).
Fergus Duniho's extrapolation from Cannon to Arrow inspired my own use of weapon names for further Hopping pieces (06).
John Savard's Bat inspired my set of reserved endings for compounds of pieces with SOLL ratios of 1 and 2 (03, 18).
Peter Aronson, Ralph Betza, and Jörg Knappen's pages on non-Straight pieces helped keep pages 09 and 13 relatively simple.
Gavin Smith's Planar pieces formed the foundation for my larger list (15).
Helen Goldhawk's name inspired the Goldhawker, Silverhunter, Brassrelayer, Azuresprinter, et cetera (21).
Daniil Frolov triggered me to fast-track a pentagonal geometry different to his (all) and devise distinctive names for Cannon/Arrow/Sling compounds with oblique pieces (08), and has produced interesting uses of unusual pieces.
John Smith (Chess variant developer) suggested Proselyte for the Crooked Panda and thereby inspired the likes of Bellerophon (09).
Joe Joyce's comment that my Fore- and Hind- pieces reminded him of Larry Niven's Ringworld inspired my Puppeteer pieces (12).
George Duke encouraged me to push square-board pieces to longer-coordinate 11 (03), and the Falcon of his Falcon Chess inspired my Vulture, Kite, and many others (13).
Tim Stiles' Wolf and Fox inspired my Jackal, Hyena, and many others (13).
Jose Carrillo's Ajax pieces inspired my Teucer, Trambelus, and Telamon pieces and their riders (02).

Authors/Composers:
Gilbert Keith Chesterton's short stories inspired the strong alliterative streak in the page titles.
René Goscinny and Albert Uderzo's Asterix books inspired the title of page 02.
Frank Lebby Stanton, one of whose songs gives (adjusted to standard English and used in a dialect-neutral sense) the title of page 09.
Russell Ash's works mentioning the "Long-nosed general" inspired the title and pig pieces of page 11.
Robert Thouless' book Straight and Crooked Thinking inspired the title of page 13.
William Gilbert and Arthur Sullivan's opera The Mikado inspired the title of page 21.
Charles Dodgson alias Lewis Carroll inspired pieces such as the Albatross (03), Umbrella (05), Walrus (06), Carpenter and Beaver (08), Bellman and offshots (10), Baker (14), and Rattlesnake (20).
John Ronald Reuel Tolkien inspired piece names such as Elf (05), Dwarf (09), Hobbit (13), Cram (12), Brook (12, via Stockbrook on 15), Denethor (16), Oldbuck (17), and Ent/-moot (18, 20).
Johann Strauss (the second), Karl Haffner, and Richard Genée's opera Die Fledermaus inspired giving Flittermouse-based pieces the names Aria (05) and Operahat (18).
William Shakespeare inspired piece names such as Oberon (05), Puck (09), and after various tragic characters (20);
Charles Dickens inspired the Pocket's compounds with the Picket and/or Packet (06);
Rudyard Kipling influenced the name Balloon (06) and the suffix -ranker (12).
Jean De Brunhof's Babar stories inspired my Celeste piece (06);
Terry Pratchett's various Zombie/Golem/Vampire characters inspired pieces of those names (06, 14).
Alfred Sherwood Romer's book Man and the Vertebrates gave names of, or connected through, extinct mammals (11, 20).
Alan Alexander Milne inspired the name of the Heffalump piece (14).
Wolfgang Mozart and Emanuel Schikaneder's opera The Magic Flute inspired names for Drumstick compounds (17).
Edward Lear inspired the name of the Akond piece (20).

Setup

GLOSSARY
Ally (02): a piece in the same ARMY.
ARMY (01): all the pieces moved by the same player, or by a team of players where pieces are not player-specific. A piece reintroduced from capture is considered to have changed army.
Beatified (06): a divergent STOPPING PATTERN, Riding when capturing else Hoppered.
Bend orthogonal: a chain of orthogonally-adjacent cells on a SerPent board running between the back-right and frtont-left corners of the board.
Bent (09): a PATH that is Straight except for a turn at the first or penultimate cell.
Binding (01): the subset of the board to which a piece is BOUND.
BOUND (01): usually of symmetric or part-symmetric pieces, able to reach only part of the board. Thus the Bishop is bound to alternate, and the Unicorn to one in four, cells of a rectilinear board.
Camp (06): the area where an ARMY starts, generally taken to be a convex area including initially empty cells flanked by two or more initially occupied ones. Thus in Shogi a player's camp is taken to include their first three ranks in their entirety.
Canonised (06): a divergent STOPPING PATTERN, Hoppered when capturing else Riding.
Capturing (02): of a move, resulting in the removal of an enemy piece, usually at the last cell of the move but sometimes en route or even beyond.
CL (13): abbreviation for Cycle Length
CMD (13): abbreviation for Cyclic Move Direction.
Colourbound (01): BOUND to alternate cells of a rectilinear board as the Bishop, Ferz, and Camel are.
Colourswitching (01): SWITCHING between the two bindings of a Bishop on a rectilinear board as the Wazir and Knight are.
Coordinate (03): the distance that a rectilinear piece moves along each orthogonal, or that a hex-prism piece moves along the interhex orthogonal and the hex plane. Standard diagonals have two, and cubic nonstandard diagonals three, equal coordinates.
Coprime (01): a Straight PATH passing only through the centres of cells where the piece can stop. So named from the coordinates of each step or leap being coprime in the mathematical sense of having no factor common to all.
Corkscrew (13): a PATH repeating steps or leaps in three or more directions in the same order.
Corner (01): a square ORIENTATION where players face along a standard diagonal. This direction os their forward diagonal and its coordinates forward orthogonals.
Corner-column (01): a cubic ORIENTATION where players face along a standard diagonal. This direction's coordinates are forward orthogonals, that diagonal and those with a forward orthogonal as a coordinate their forward standard diagonals, and nonstandard diagonals with both forward orthogonals as coordinates forward nonstandard diagonals.
Crooked (09): a PATH alternating between steps or leaps in two directions by making opposite turns at the end of each.
Cubic (01): a 3d GEOMETRY with 6 orthogonal, 12 standard diagonal, and 8 nonstandard diagonal directions. 2 cubes meet at a face, 4 at an edge, 8 at a corner. Radials are orthogonal,standard diagonal, and nonstandard diagonal.
Cycle Length (13): the number of directions used by a Corkscrew piece before repeating the first direction again.
Cyclic Move Direction (13): the direction of a Straight path between cells of the PATH of a given Corkscrew piece at intervals of the Cycle Length.
Curved (09): a PATH repeating turns of the same kind - in 2d, all left or all right - at the end of each stage, so that a long enough move (if allowed) will bring it back to where its move starts.
Destination (09): a cell which a piece can reach in a single move.
Diagonal (01): generic for radials other than orthogonals.
Divergent (02): differing in noncapturing and capturing moves, usually between different types of RADIAL (as with Pawns) or different STOPPING PATTERNS (as with Cannons).
Double Bent (09): a PATH that is Straight except for turns at the first and penultimate cells.
Doubly oblique (14): of oblique pieces on hex-prism boards, having a hex coordinate that is itself oblique.
Dual (03): in the square GEOMETRY, one of two (usually coprime) pieces with a SOLL ratio of 2 because for each move of the odd-SOLL piece to a destination m:n away the even-SOLL one has a move to one m+n:m-n away. On cubic boards this extends to the relationship between the 2:2:1 and 4:1:1, and between the 6:3:2 and 8:5:3, leaps and across the cubic-hex divide to m+n:m:n cubic leaps and hex ones with half their SOLL. Hex boards on their own have an analagous but less useful duality based on SOLL ratios of 3.
EMD (09): abbreviation for Even Move Direction
Enemy (02): a piece of a different ARMY.
Even Move Direction (09): the direction of a Straight path through alternate cells of the PATH of a given Crooked piece.
Face-to-face (01): a rectilinear ORIENTATION where players face along an orthogonal. This direction is their forward orthogonal and any diagonals of which it is a coordinate are forward diagonals.
File: a series of cells directly forward and backward in face-to-face rectilinear, Glinsky hex, and Glinsky-level and hex-ranked hex-prism boards.
File diagonal: a chain of diagonally-adjacent cells on a SerPent board running forward and backward.
File orthogonal: a chain of orthogonally-adjacent cells on a SerPent board running forward and backward with negligible net sideways movement.
Filebound (01): BOUND to alternate files of a board as the Dabbaba, Elephant, and Glinsky-ORIENTATION Moorcock are.
Filestack (12): a series of files directly above and below each other on a 3d board.
Fileswitching (01): SWITCHING between odd and even files as the Ferz and Camel are on 2d and Glinsky-level boards and the Viceroy and Elf on cubic ones.
Forward-only (01): a SPAN covering only moves that are more ranks forward than files sideways - or up or down.
GEOMETRY (01): the shape and arrangement of cells on the board. 2d geometries include square and hex. 3d geometries include cubic, hex-prism, and xyrixa.
Frolov Pentagonal (01): a particular Pentagonal GEOMETRY in which the two other cells diagonally adjoining a cell do so at corners sharing an edge. This and the next might be renamed if Mr. Frolov himself can devise a snappier term.
Frolov-Pentagonal-prism (01): a particular Pentagonal-prism GEOMETRY whos levels are Frolov Pentagonal boards, stacked so that each cell is on a normal Straight orthogonal at right angles to the Pentagonal plane.
Glinsky (01): a hex ORIENTATION where players face along an orthogonal. This is their forward orthogonal and the two nonstandard diagonals flanking it their forward diagonals.
Glinsky-level (01): a hex-prism ORIENTATION where players face along an orthogonal parallel to the hexagonal faces. This is their forward orthogonal, the two standard diagonals above and below it their forward standard diagonals, the two nonstandard diagonals flanking it their forward nonstandard diagonals, and the four hybrid diagonals above and below those their forward hybrid diagonals.
Half-backward (12): the two orthogonals on a Glinsky, or nonstandard diagonals on a Wellisch, board that are more sideways than backward.
Half-forward (12): the two orthogonals on a Glinsky, or nonstandard diagonals on a Wellisch, board that are more sideways than forward.
Half-left (12): the two orthogonals on a Wellisch, or nonstandard diagonals on a Glinsky, board that are more forward or backward than left.
Half-right (12): the two orthogonals on a Wellisch, or nonstandard diagonals on a Glinsky, board that are more forward or backward than right.
Hex (01): a 2d GEOMETRY. Cells are hexagons with 6 orthogonal and 6 nonstandard diagonal directions. 2 hexagons meet at an edge, 3 at a corner. If "2d or 3d" is specified, includes hex-prism and xyrixa.
Hex-level (01): generic for the Glinsky-level and Wellisch-level ORIENTATIONS.
Hex-prism (01): a 3d GEOMETRY. Cells are prisms with six square and two hexagonal faces. There are 8 orthogonal, 12 standard diagonal, 6 nonstandard diagonal, and 12 hybrid diagonal dircetions. 2 prisms meet at a face, 3 at an edge of two square faces, 4 at an edge of a hexagonal face, 6 at a corner.
Hex-ranked (01): a hex-prism ORIENTATION where players face along the interhex orthogonal. This orthogonal is their forward orthogonal, and the six standard diagonals of which it is a coordinate their forward standard diagonals.
Hop (06): to pass through an occupied cell as a necessary part of a move. The Hopped piecw is sometimes termed a Screen or Hurdle. For the Hopping piece see the participle itself.
Hoppered (06): a STOPPING PATTERN repeating several steps or leaps through cells of which a set nonzero number (usually 1) are occupied and the rest empty.
Hopping (06): generic for Beatified, Canonised, and Hoppered STOPPING PATTERNS. A Hopping piece should not be confused with a Hoppering one, a special case of a promoting piece conferring a Hopping move on an ally.
Hybrid Diagonal (10): a type of RADIAL specific to the hex-prism GEOMETRY with a SOLL of 4. So called because it has both a hex and a rectilinear element.
Hypotenuse piece (05): with respect to a pair of duals or semi-duals, a third even longer-range piece whose leap is equivalent to one leap of each at right angles.
Initial move (02): a special move allowed for a Pawn or similar piece early in its trek to promotion, in order to speed up the opening of a game.
Interhex (14): in the hex-prism GEOMETRY, the ORTHOGONAL at right angles to the hex plane.
LEAP LENGTH (03): the length of a Straight piece's shortest move as a multiple of the length of the GEOMETRY's shortest move. See also SOLL.
Leaping (03): a STOPPING PATTERN moving directly between two non-adjacent cells.
Level (01): a series of cells the same distance above the surface on which a 3d board rests.
Levelswitching (01): SWITCHING between odd and even levels as the Ferz and Camel are on hex-level hex-prism boards and the Viceroy and Elf on cubic ones.
Long-range (01): being able to move an indefinite distance, limited only by board size and blocking pieces. Thus a Rook can move 7 steps on an 8x8 board, but this lengthens to 15 on a 16x16 board.
Mixed-range (01): being the compound of a long-range and a short-range piece, typified by Shogi's promoted linepieces.
ND (01): abbreviation for Nonstandard Diagonal.
Non-coprime (06): a Straight PATH passing through the centres of cells where the piece cannot stop. So named from the coordinates of some steps or leaps being non-coprime in the mathematical sense of having a factor common to all.
Noncapturing (02): of a move, not resulting in the removal on an enemy piece whether at the last cell of the move (which must be empty) or elsewhere.
Nonstandard Diagonal (01): any RADIAL with a SOLL of 3, including cubic ones with three equal coordinates and the only type of 2d hex diagonal. The cubic one is colloquially known as triagonal, but this name is not universally accepted.
Oblique (03): a direction other than a RADIAL. Oblique directions are so numerous that rather than having names like those of the radials they are described in terms of their coordinates. The 2:1:0 Knight, 3:1:0 Camel, 3:2:0 Zebra, 2:1:1 Sexton, and 2:2:1 Ninja are typical oblique pieces.
ORIENTATION (01): how a board of a given GEOMETRY is turned relative to the players, determining the concept of forward moves. Backward, left, right, and in 3d cases up and down are defined as rotations of the forward directions.
Orthogonal (01): any RADIAL joining adjacent cells through the centres of, and usually at right angles to, their boundaries - edges in 2d, faces in 3d. The distance between orthogonally adjacent cells is the shortest distance between any cells in the GEOMETRY, and in those with which this series deals every SOLL is an exact multiple of the square of this minimum distance.
Part-coprime (06): the PATH of the compound of a coprime and a non-coprime piece, typified by the Waffle and Squirrel.
Part-symmetric (04): the SPAN of the compound of a symmetric and a forward-only piece, typified by Shogi generals.
Pentagonal (01): any 2d GEOMETRY in which the cells are pentagons.
Pentagonal-prism (01): any 3d GEOMETRY whose levels are pentagonal boards, stacked so that each cell is on a normal Straight orthogonal at right angles to the Pentagonal plane.
Planar (15): a PATH requiring a piece being able to reach a cell only if all available shortest routes are empty.
Promotable (01): able to be promoted. Note that promotable pieces are distinct from the Promoting ones of page 21, which promote other pieces.
Promote (01): to end a move with the changing of a piece, usually the one moved, into a piece of another type. The new piece type is either a stronger one, at least locally (as in the case of Shogi), or one that further promotion at a later stage will strengthen in the long term. Promotion may be represented physically by subsituting the usual (or an improvised) representation of the stronger piece (FIDE Chess), flipped over to display the symbol for the new piece (Shogi), or determined purely by position (Xiang Qi).
RADIAL (01): a direction passing through the centres of all cells whose interiors it passes through.
Rank (01): a series of cells the same distance forward from the player in face-to-face rectilinear, Wellisch hex, and Wellisch-level and hex-ranked hex-prism boards.
Rank diagonal: a chain of diagonally-adjacent cells on a SerPent board running sideways.
Rank orthogonal: a chain of orthogonally-adjacent cells on a SerPent board running sideways with negligible net forward or backward movement.
Rankbound (01): BOUND to alternate ranks of a board as the Dabbaba, Elephant, and Wellisch-ORIENTATION Moorcock are.
Rankswitching (01): SWITCHING between odd and even ranks as the Ferz, Camel, and Silvergeneral are on 2d, Wellisch-level, and hex-ranked boards and the Viceroy and Elf on cubic ones.
Rectlinear (01): generic term for the square GEOMETRY in 2d and cubic one in 3d.
Reflecting (15): a PATH bouncing off the edges of a 2d, or the edges and faces of a 3d, board.
Refracting (15): a PATH turning through the long diagonals of a 2d, or long-diagonal planes of a 3d, board.
Rider (02): relative to a Stepping or Leaping piece, a corresponding Riding piece, the Straight one unless otherwise qualified.
Riding (03): a STOPPING PATTERN repeating any number of steps or leaps through empty cells.
Rotated Frolov Pentagonal (01): a particular Pentagonal GEOMETRY in which the two other cells diagonally adjoining a cell do so at corners sharing an edge. This and the next might be renamed if Mr. Frolov himself can devise a snappier term.
Rotated Frolov-Pentagonal-prism (01): a particular Pentagonal-prism GEOMETRY whose levels are Frolov Pentagonal boards, stacked so that each cell is on a normal Straight orthogonal at right angles to the Pentagonal plane.
Royal Restriction (01): a bar on a player exposing a particular piece to capture, as applies to the King. A piece with a royal restriction generally differs in name from an identically-moving capturable piece.
Scarp orthogonal: a chain of orthogonally-adjacent cells on a SerPent board running between the back-left and frtont-right corners of the board.
SD: abbreviation for Standard Diagonal.
Semi-Dual (05): in the cubic GEOMETRY, one of two (usually coprime) pieces with a SOLL ratio of 2 because for each move of the shorter-range piece to a destination m:m:n away the longer=range one has a move to one 2m:n:n away.
SerPent (01): a particular Pentagonal GEOMETRY in which the two other cells diagonally adjoining a cell do so at corners not sharing an edge.
SerPent-prism (01): a particular Pentagonal-prism GEOMETRY whose levels are SerPent boards, stacked so that each cell is on a normal Straight orthogonal at right angles to the Pentagonal plane.
Short-range (01): having a set maximum move length however large the board. Thus the Knight is only a 2:1 leaper, even on a 16 by 16 board. Includes steppers, leapers, Hopping versions thereof, and compounds thereof.
Singly oblique (14): of oblique pieces on hex-prism boards, having their hex coordinate a nonstandard diagonal.
Square (01): a 2d GEOMETRY. Cells are squares with 4 orthogonal and 4 standard diagonal directions. 2 squares meet at an edge, 4 at a corner.
SOLL (03): Square of LEAP LENGTH, a number that is always an integer. In rectilinear GEOMETRIES it is the sum of the squares of the coordinates.
Standard Diagonal: any RADIAL with a SOLL of 2. So called because it is the diagonal in regional standard games such as FIDE Chess, Shogi, and Xiang Qi.
SPAN: which subset of a type of direction a piece moves in. Pieces can be symmetric, forward-only, part-symmetric, or more complex.
Stepping (03): a STOPPING PATTERN making a preset number of steps through empty sets along one or more RADIALS. Avoid using lame as a synonym, as its pejorative connotations can offend Stepper enthusiasts.
STOPPING PATTERN: which cells along its path a piece can stop on and which may, or need be, empty or occupied.
Straight (01): any PATH continuning in a single direction with no turns.
Straight Backward (12): the orthogonal on a Glinsky, or nonstandard diagonal on a Wellisch, board that is backward but not sideways.
Straight Forward (12): the orthogonal on a Glinsky, or nonstandard diagonal on a Wellisch, board that is forward but not sideways.
Straight Left (12): the orthogonal on a Wellisch, or nonstandard diagonal on a Glinsky, board that is left but not forward or backward.
Straight Right (12): the orthogonal on a Wellisch, or nonstandard diagonal on a Glinsky, board that is right but not forward or backward.
Switchback (13): a PATH alternating between steps of a Straight path and of one that is itself Crooked, usually moving in the direction of the Straight piece every 4 steps.
SWITCHING (01): able to move only from one subset of the board, or of its binding if bound, to the rest of the board or binding. This restriction prevents a piece returning to a cell in an odd number of its own moves.
Symmetric (01): a SPAN including all directions of a type. Thus a Knight can move 2 ranks either way and 1 file either way, or vice versa - and in 3d many futrher ways.
Triangulate (01): of a piece, to return to a cell in three of its own moves. If null moves are barred this is the smallest odd number of moves in which any piece can return to a cell. Symmetric short-range pieces that can triangulate include all on a Hex 2d board, compounds of duals on a square 2d board, and m+n:m:n leapers on a cubic 3d board.
Turn (09): the angle by which a non-Straight piece's PATH rotates at intermediate cells - that is, the angle between the new direction and the Straight continuation of the old one, so that a piece turning more than 90° is to some extent turning back on itself.
Unbound (01): usually of symmetric or part-symmetric pieces, able to reach the entire board.
Unswitching (01): of a piece, able to return to a cell in an odd number of its own moves.
Wellisch (01): a hex ORIENTATION where players face along a nonstandard diagonal. This is their forward diagonal and the two orthogonals flanking it their forward orthogonals.
Wellisch-level (01): a hex-prism ORIENTATION where players face along a nonstandard diagonal. This is their forward nonstandard diagonal, the two orthogonals flanking it their forward orthogonals, the two hybrid diagonals above and below it their forward hybrid diagonals, and the four standard diagonals flanking those their forward standard diagonals.
Xyrixa (01): a 3d GEOMETRY. Cells are rhombic dodecahedra. There are 12 orthogonal, 6 standard diagonal, and 24 nonstandard diagonal directions. 2 cells meet at a face, 3 at an edge, 4 at an obtuse corner, 6 at an acute corner. Named after an obscure variant invented long before, but apparently using the same board as, Mark Thompson's Tetrahedral Chess.