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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 2011-02-26 UTC
Whatever the initiating reason that propelled him, there become many reasons for Betza to stay 64-bound. ''64-only'' is his artform in itself, art pour l'art. Betza never made Xiangqi variant, Shogi variant, or Hexagonal. Or did he hexagonal? Even the one Hexagonal here Betza makes 64-spaced out of respect for the venerated dying 1400-year board tradition that size. 75% of Betza cvs appear to come after year 1995, though arguably majority of his classics are among the earlier 25%. The Betzan size (of 64) is less important than the boards of any other past prolificist during their heyday. That is because after 1999, they are concept-cvs, basically clever Mutators, sometimes brilliant, Mutators like Neto's, linked at the end. Neto different-styled is content to list them extensively, whilst Betza, entertaining and deceptively guileless, obsesses to embody them one and all. That practice is carried on by others. Usually it is hard to distill a sure coherent rules-set because Betza's are deliberately multiple even exponential, suggesting hundreds of variants in the same one cv write-up. Augmented Chess article counts 560 different armies. He gets away with that rarely becoming tiresome, never expecting most to be played. (his own refrain: ''I have not played this but....'') Exceptions include Nemeroth, which so complicated points to its sole interpretable rules-set only. [ Neto's 40 Mutators taken 2 at a time legitimately belong to himself as author alone. If he had wanted to take the time, instead of this article he could have written up 1560 separate cvs in the prolificist era or the follow-up post-your-own era, Fine_Mutators_by_Neto. Neto has both more sense and more courtesy not to proceed the other way than this concise article. ]

George Duke wrote on 2010-11-15 UTC
Thanks Joe Joyce and Ben Reiniger. Great there are more than one way to win a matt, schachmatt. Here is another argument the same as or overlapped with yours.  TRIANGLES OF THE MIND.  Of course the complete triangular grid is already there inside the square. Just take Betza's first step, rotating the utility board 45 degrees. Do not perform Recta-hex-ing, stop at Betza's first sentence.  Give each Square/Diamond a top-half and bottom-half. That object then has all the features of equilateral triangular grid linked,, since different angles 90, 45 and line lengths topological equivalence dissolves. Then require each piece entered into the space be positioned close to either an ''up-vertex'' or a down-vertex slot, so the two dimensions, conjuring infinitesmals, do not ramify to anything as significant as ''triangle.'' Each cell to play, insofar as it has minimal practical room for piece-marker, must needs have/be an up-vertex area or else a down-vertex and never both. No triangles are involved or ever required to be drawn or even pictured. Play within squares from vertex area to vertex area. Keep looking at squares only and play Chess (Variants). That way the Anti-Triangular board is made only of the everlasting same 64 2^6 squares (and Checkers 100 10^2 squares for enlargement). __________________________________Since we are only using squares, the regular 64 of them, movement has to be carefully defined.  Each move begins and ends into up-vertex slot or down-vertex slot, never something like phony ''side-vertex.''  The latter does not exist.  Remember to keep the board with diamond orientation. Thus 64 ''squares'' are 128 vertex-locales, more than enough. Each up-vertex is unique, so it has a number like '9', Cell 9.  From '9' there are four equidistant other up-vertices lettered 'a' to 'd' CW from top.  They are a square side-length away.  The first one of them, 'a', is actually top-off-center right. And so on with down-vertex locations we want to fulfill from a starting cell.  Play from up-vertex cell to down-vertex and vice versa, and up to up and down to down, completing all the possibilities relatively nearby, for defined piece-types.  Each sub-space/cell is as that infinitesmal building towards a point(corner of Square) and has no dimension except created by convenience in marking. Bi-colouration of the board may tend to distract and can be eliminated. So long as the divisible, exactly-delineated space is elementary/fundamental, Rules then can achieve the full degree of decadent over-refinement customary to CVers. Watch your step. These proofs are not semantic; is not all space everywhere one-dimensional-acquired directionality? Summary: Hexagonal -> Rectahex -> Square -> Triangle (reversible).  The only trick is the Rectahex slide a la Betza.

Ben Reiniger wrote on 2010-11-13 UTC
Another way to get triangular is by playing on the corners of a hex grid, so you could use the rectahex board in the same fashion; you just have to be able to remember that the intersections of a vertical edge with what appears to be a square's edge is actually another corner (since the apparent edge of the square is in fact two separate edges in the rectahex sense).

Looking a bit more closely though, this won't work if the board is turned around in the 'proper' orientation.  Notice that the corner of the hexes d4,d5,e4 should be adjacent to the corner of the hexes d5,e4,e5; but on the usual orientation these are the same corner!  You could get around this I suppose, but it would be ugly.

Joe Joyce wrote on 2010-11-13 UTC
To answer your question about squares used for triangular movement:
You remove some of the squares in a particular pattern. Each removed square is at the center of a hexagonal arrangement of squares that are always present. Pick any square from that always-present hex arrangement of squares, and remove neighboring squares such that any is always surrounded by an alternating pattern of present and absent squares. 

This pattern allows triangular movement, some of which may pass through the absent squares to the present squares on the other side. This pattern leaves the board with these features:
1 - all absent squares are at the center of a hexagonal ring of present squares. 
2 - All present squares are members [junction points] of 3 rings of present squares. 
3 - All present squares have 3 absent neighbors, and 3 present neighbors.

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 2009-01-22 UTC
Ralph Betza's diamond, Betza ostensibly rotated after Hitchhiker and also after Aiken's Double Diamond (the only game on 73) and Mills' Diamond of 40. Betza's is the best of them both artistically and playably, since as usual Betza gives alternative(s) bringing the idea to fruition, well beyond Legan that Brainking dully plays.

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.

Tony Paletta wrote on 2003-05-08 UTC
In mentioning a three-geometry game, I meant a game which incorporated
piece movements derived from hexagon-tiled, square-tiled and
triangle-tiled chess variants. The board itself would involve one

Consider a 12x12 board tiled with equilateral triangles (all have a one
horizontal side, a1 points at W, a2 at B, a3 at W ..., b1 points at B, c1
at W, etc.). Triangle chess movement (as in Dekle's Triangular Chess -
see Pritchard's Encyclopedia of Chess Variants) would be based on the
shapes, standard chess movement on the ranks and files (N leaps 2 ranks, 1
file or 2 files, 1 rank; R slides along rank or along file; B leaps in
1r,1f steps in same direction, etc.) and hexagonal movement would follow a
scheme similar to that in Hexoid Chess (/Rectahex Chesss). A hex-style
three-coloring of the board (a1-blue, a2-yellow, a3-red, a4-blue, ...
b1-yellow, b2-red, b3-blue, b4-yellow, ..., c1-red, c2-blue, c3-yellow,
...) would help a little for the hex movements.

On such a board we could have Standard Knights, Triangular Queens and
Hexagonal Rooks, etc. cheerfully (?) coexisting. Getting the hang of the
game would be a little tough -- but then again, who ever said unified
(playing) field theory would be easy?

TBox wrote on 2003-05-08 UTC
Two in a row! Sorry, sorry. I think the *best* usage of Rectahexahexarect chess is to win bets. Introduce it to your 'friends', but change its name and leave out its origin. While they're struggling with their crib notes on piece movements and nigh impossible tactics, you're playing a variant of Alice hex chess where pieces can take pieces on the other board by occupying the corresponding square. (Use markers to show these 'ghosts') This requires correspondence play, of course.

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.

gnohmon wrote on 2003-01-16 UTC
If I have inspired Trigon Chess, then I count RectaHex as a success, a
veritable succectahex.

I first read of Glinski's game in my tattered copy of Boyer, with the
diagram of 'Echecs Hexagonaux de W. Glinski' right there on the cover; and
I always felt there was something wrong about the game. The rationale for
why the pieces move as they do is so logical and convincing that it is
hard to question the game; but something is wrong somewhere.

Perhaps Glinski is fine as is, but Rectahex should spur some new thinking.

Tony Paletta wrote on 2003-01-16 UTC
Glinski-type bishops can reach every third diagonal, so if the standard chess array position is used both bishops are limited to the same 1/3rd of the board.

tony paletta wrote on 2003-01-15 UTC
Should compare this to my Hexoid Chess and Rex Chess (both hexagonal on 8x8
standard chessboard) or Tetragonal Chess (more an inspired by; rotate the
board, but retain hex-type movement) -- all 'modest chess' variants (piece
variants) buried somewhere on CVP. One difference: I use Q as a third
bishop to offset bishops only covering 2/3 of board in Hexoid Chess (and
also because Glinski-type hex-Q is a killer on 8x8 board). I also felt
that directions are much easier if board is rotated 45 degrees, so a1
points at White.

By the way, a similar translation can be made for 'Triangular Chess':
imagine all dark squares are equivalent to equilateral or isosceles
triangles with edges horizontal and 'pointing' at Black. Pieces move
differently on dark squares than on light squares -- on dark squares on
type of N is >Black as [v2, h1], >White as [v1, h2] and horizontally as
[h3, v0], and reverses White-Black move pattern if on a light square.
Probably no more than one Trigonite type per game is best (Trigonic Knight
Chess?). Reversing imagined direction of 'pointing' gives a second type of
crabbish Knight.

This opens up the possibility of a three-geometry chessboard game -- if
only as a sort of unified (playing) field theory.

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!

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