[ Help | Earliest Comments | Latest Comments ][ List All Subjects of Discussion | Create New Subject of Discussion ][ List Latest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]Rated Comments for a Single ItemLater ⇩Reverse Order⇧ Earlier Rectahex Chesss. A chess variant that looks like hexagonal chess but can be played on a normal chess board. (8x8, Cells: 64) [All Comments] [Add Comment or Rating]George Duke wrote on 2010-11-12 UTCExcellent ★★★★★(1)What Rectahex comes down to needs no higher math or Betza master-skill spatial intuition. Simply put, sawtooth the board. That is, saw-tooth any rectangular board. Get the sides/edges how you want them artistically for however many squares. Now each interior square has six others adjacent, so it functions topologically hexagonally just as well even without deformation of the cell itself. Betza's article's end/beginning, ''Is hexagonal chess really hexagonal, or is it merely a rectangular dream?'' is so much poetical locution reflective of one combined state. Discard any construction half-fits left over from the work-ups, having slid and sized to requirement. In ideal material, actually just stretch and bend each square to a regular hexagon careful not violating even one adjacency. TOPOLOGICAL EQUIVALENCE. One size fits all. One board, and only one, serves both squares and hexagons of same number cells or smaller (black tape reductions). Make it 196 spaces of sawtooth 14x14 and that is 99.5% of the world's CVs ever made. _______________________________________________________________ (2) For purists over-the-board ideal material must needs be out there to shapeshift easily square-to-hexagon-to-square as rules-sets demand. CLAY takes some doing and Rectahex Ascii above shows is unnecessary routinely. For follow-up, how also can rectangles comprised of squares, whether or not saw-toothed, minimally disrupted, best reflect TRIANGULAR connectivity? This problem re-stated: We want not to draw a single triangle as such, yet have now more prevalent cultural squares represent them and their inter-connections accurately and completely. ___________________________(3) ENVOI. Thus squares may be at a crossroad, why Chess square-based remains. In the real world, more squares surpass circles and triangles for now, contrasted to superior antiquity (See Armies of Faith series). Just try stepping out to the market without an inefficient right-angle turn. Virtually impossible. Prevalent 90 degrees: house, room, that still monitor, blocked neighborhoods. Pourquoi? Obviously convenient states ''their'' Squares for control such that nary a soul be seeing/seen/scene/scheming/seeming around the corner. George Duke wrote on 2007-11-02 UTCExcellent ★★★★★Looking like Balbo's Chess, Rectahex Chess with non-edge cell having six adjacent cells becomes isomorphic with standard Hexagonal Chesses under Ralph Betza's treatment. ''Hexagonal Chess can be played quite simply on a normal rectangular board.'' However, Phil Brady says 5 years ago, ''The advantage of playing with hex-moving pieces on a readily available rectangular board is outweighed by the complexity of biasing the board to match the connections of a hexagonal one.'' The obligatory scads of variates include Rectahexahexarect, replacing a Rectahex piece with its Hexarect equivalent at option, and vice versa. David Paulowich wrote on 2007-06-05 UTCExcellent ★★★★★Fergus Duniho illustrates the 12 directions of movement on a hexagon board and inteprets them for Shogi pieces on his Hex Shogi page. In Hex Shogi 81 he copies the traditional Shogi setup to a 'tilted rectangle' made up of 81 hexagons. A few weeks ago I was looking at Duniho's game and thinking that it could be also played on a square board, with a little mathematical magic. It should be possible to use Ralph Betza's work to accomplish this task. Start with a traditional Shogi board and pieces. Replace the Rooks with 'Rectahex Rooks' and the Bishops with 'Rectahex Bishops'. Looks like the Shogi Knight can be replaced by a Rectahex Knight, restricted to four forward Bison moves. In the final analysis, pieces are completely defined by their movement rules - the geometry of the board is merely a convenient aid to play. But I am not seriously recommending that anyone try to play a game of Rectahex Shogi 81. Abdul-Rahman Sibahi wrote on 2007-05-28 UTCGood ★★★★I like this game !! I have an observation. If we merge the board rotated to the right with the board rotated to the left, We get Queens for Rooks, Unicorns (BNN) for Bishops, and NJZ (Knight + Camel + Zebra) for Knights, Queen of the Night (BRNN) for Queen. Sounds like a nice variant. If we subtract the original pieces movements from Rooks, Knight, and Bishops, we get Bishops for Rooks, Bisons for Knights, Nightriders for Bishops, and Unicorn for Queen. This makes a nice CwDA army. Don't you think ? I will post this into a new page, since it is a very different variant. TBox wrote on 2003-05-08 UTCExcellent ★★★★★I'm most likely misunderstanding what Tony Paletta means by a three-geometry chessboard game, but I'm going to pretend it means a chessboard with three different types of square. Actually, there's four, look: <pre> --------------------- | | | | | | | | | | --------------------- | | | | | | | | | | --/-\----/-\----/-\-- /\/ \/\/ \/\/ \/\ /--\ /--\ /--\ /--\ / \ / \ / \ / \ \ /-\ /-\ /-\ / \--/ \--/ \--/ \--/ / \ / \ / \ / \ / \ / \ / \ / \ \ /-\ /-\ /-\ / \--/ \--/ \--/ \--/ \/\ /\/\ /\/\ /\/ /--\-/----\-/----\-/-- | | | | | | | | | | -------------------- | | | | | | | | | | -------------------- </pre> For the ASCII Art impaired, a verbal description: The top and bottom two ranks have 9 files, and are regular squares. Bordering files a, c, d, f, g, and i are equilateral triangles. Bordering files b, e, and h are regular hexagons. Between the triangles on files c and d, and files f and g, is a triangle facing the opposite way. Two more triangles are placed next to the leftmost and rightmost triangles. These two triangles face opposite to the triangle they are next to (regular trigon tesselation).<p> Above the row of hexagons and triangles is a crooked row of seven hexagons in regular tesselation. This pattern is half the board. Create a mirror image facing the other way, and join the two halves such that the three soon-to-be-center-most hexagons overlap. Despite the ASCII, all squares are the same size, all hexagons are the same size, and all triangles are the same size.<p> I can think of tons of variations on this board, mostly by adding, removing, or replacing hexagons with triangles or vice versa.<p> My question: How would the pieces move? Here's what I think:<p> The Rook, as its first step, can move to any cell which shares a border with its current cell. Its second and subsequent steps must be to the cell whose border is directly opposite the border it entered from. Triangles don't have an opposite, so they require some obnoxious rules. There are two kinds of triangles: Attacking (with points towards your opponents) and Defending (with points towards yourself). It is the nature of the board and the rook move that it must alternate between attacking and defending triangles, no matter how many cells of other shapes lie in between. Because of this, I will define the step by calling them Odd and Even triangles. The Odd triangle is the *first* triangle you move *to* in a rook move. When entering an Odd triangle, pretend the border you entered on is connected to an Even triangle (even if it is a square or hexagon). The next time you enter an Even triangle, the only way to continue your move (if you wish) is to exit by the same border as the imaginary triangle you exited when you first entered the original Odd triangle. By leaving the Odd triangle, you similarly define the border by which you must exit (if you choose to continue your move) the next Odd triangle you enter.<p> Bishops. If the cell you are currently in is a Square or Triangle, valid directions for a bishop are those cells which touch your current cell, but a Rook cannot reach (That is, they share a corner). Unfortunately, this would trap the Bishops on their respective sides, because the Rook can reach all the hexagons surrounding a hexagon. I could alleviate this by replacing the three central hexagons with rings of triangles, but then the board 'degenerates' into an 8 rank board with 4 ranks of 9 files on the edges, and 4 ranks of 13 files in the center, with some odd connections at the seam. Instead, I will say (generically) that if two of the cells a rook can reach in a single step share a border, then the bishop can jump to the nearest square in the same direction as the shared border (that is also not one of the two original cells). (There *has* to be a simpler way to say all that). For subsequent steps, if you are on a square or hexagon, you must leave to the first available square in the direction of the corner opposite the one you entered by. Theoretically, similar 'marking' rules as the Rook can be used for the triangles, but in practice, it makes my head hurt. <p>The queen would simply combine rook and bishop. <p>The knight would be able to leap to the nearest N squares which cannot be reached by the queen (rook or bishop), and whose manhattan distances all share the same value. For purposes of manhattan distances, the distance between the center of two cells which share a complete border is the same for any combination of cell shapes. (Not that that's possible to *draw* without seriously skewing the board). <p>After examining some of the possible moves for this type of game, I have decided that it somewhat resembles a game of shifted square chess, which says something, I just don't know what. The triangles have a tendency to skew the movement in unusual directions, especially if a piece can choose to enter more than one triangle in a turn. Anonymous wrote on 2003-01-17 UTCExcellent ★★★★★Nice idea, very inspiring. Phil Brady wrote on 2003-01-15 UTCGood ★★★★For the sake of argument, I'll take the opposing point of view. :) 'Hexagonal Chess can be played quite simply on a normal rectangular board' is a statement not justified by the article. First the player is expected to either rotate a board 45 degrees and remember that corners are now edges and vice versa, or they need to memorize a new army unusual-moving pieces. For the author of the article these may be simple tasks, but I would venture to say that for the casual CV player it is difficult. The author even implies this himself when describing the moves of the pieces: 'This is confusing' and 'This is a cumbersome piece' are used, and the 'normal' description of how the pieces move are complex. The advantage of playing with hex-moving pieces on a readily available rectangular board is outweighed by the complexities of 'biasing' the board to match the connections of a hexagonal one. It would be to a player's advantage to buy an inexpensive set of poker chips and arrange them as a hexagon and use the 'standard' hexchess pieces. The article is useful, in that it shows how one type of board and pieces can be mapped to another type. It can provide the starting point for further hex/rect explorations, and possible new pieces for the rectangular board. 'Biased' pieces as described in the article are vaguely reminiscent of left- and right-handed pieces in shogi variants. The rectahex knight could be matched with a mirrored one to make a pair of 'ufos' on a large-board variant. Thanks for the article! 7 comments displayedLater ⇩Reverse Order⇧ EarlierPermalink to the exact comments currently displayed.