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This item is a game information page
It belongs to categories: Orthodox chess, 
It was last modified on: 2002-11-01
 By Mark  Thompson. Tetrahedral Chess. Three dimensional variant with board in form of tetrahedron. (x7, Cells: 84) [All Comments] [Add Comment or Rating]
Anonymous wrote on 2011-03-27 UTCGood ★★★★
I like the creativity in creating a colorbound piece on a board that doesn't lend itself easily to non-rook moves. Very simple, yet complex enough to offer a challenge to players. I've been halfheartedly toying with the idea of tetrahedral chess myself for a few months, and this is the first version I've seen.

George Duke wrote on 2007-11-07 UTCExcellent ★★★★★
Tetrahedra have 4 faces, 6 edges. This pyramid stands on edge instead of face. Two edge-pair's midpoints determine one line, and 2 such lines determine a plane (the 4x4 here). That cross-section is a rectangle not usually square. So are all cross-sections of all other parallel planes intersecting. Cleverly and arbitrarily, Mark Thompson chooses 5 such planes and 2 more planes fashioned out of two edges, totalling 7, in order to get notional-3D 84 spaces(year 2002 84-square contest). They then divide conveniently into two(1x7), two (2x6), two (3x5), and one (4x4) making 84. How is that related also to 84 as tetrahedral number? 84 as tetrahedral number(think sphere-stacking oranges) sequences one(1), supported by 3 making four(4), supported by 6 making ten(10)[this is experimental too], then 10 making twenty(20): 1,4,10,20,35,56,84,120... For the five piece-type differentiation, the six edges each have two directions for 12 altogether. Contrast these 12 to the 26 directions necessary for complete interpretation in awkward standard cubic chesses (6 orthogonal, 12 diagonal and 8 triagonal or trigonal). See in the tripartite diagram the distinguishment between King and Rook.

Todor Tchervenkov wrote on 2005-11-23 UTCExcellent ★★★★★
Very nice game. I like the idea of a non-cubic 3D chess variant.

Charles Gilman wrote on 2004-03-29 UTCExcellent ★★★★★
Observing that the faces of this board are hex boards, I notice that your usage of King and Knight is identical to that of S. Wellisch in the first hex variant. This shared usage is now recorded (complete with link to this page) in my piece article Constitutional Characters.

Charles Gilman wrote on 2004-01-19 UTCGood ★★★★
At last, I can see it all. It started when I noticed that on cubic 3d board, a plane including two standard (root 2) diagonals not at right angles (a) automatically includes a third, (b) comprises squares of only one Bishop colour but all four Unicorn colours, and (c) resembles a hex board. The 3d orthogonal and root 3 diagonal are lost but the root 2 diagonal becomes a hex orthogonal, the 2:1:1 (root 6) oblique a hex root 3 diagonal, and the 3:2:1 (root 14) oblique a root 7 hex oblique. Then I realised what the Tetrahedral Chess pattern of 3 diagonals mutually at right angles and 6 orthogonals each at right angles to one other and a diagonal reminded me of. It was the cubic board's orthogonals and diagonals swapped over! Yes, the Tetrahedral board can also be seen as a cubic-cell board with cells of one Bishop colour missing, and the cell notation shown actually fits with this interpretation!

Charles Gilman wrote on 2004-01-18 UTCGood ★★★★
My last comment was a quick correction/explanation of what I had said before. Now that I have had some time to think offline I can comment on the idea of splitting the the orthogonals into two groups of three. The truth is, any such division is arbitrary. They naturally divide into three groups of two - those in the horizontal plane, and those in the vertical plane through each horizontal diagonal. In fact these planes are interchangeable, each having 2 orthgonals of its own and two diagonals each shared with one of the other two. However limiting pieces to those pairs of orthogonals binds them to single planes, and even limiting them to the two orthgonals in a plane and the diagonal outside it would bind them to alternate planes. The oddity that the root-three (hex) diagonal is not colourbound on this board is matched by the root-two (square) diagonal is not colourbound on a hex-prism board.

Larry Smith wrote on 2004-01-09 UTCExcellent ★★★★★
A very nice game.  Interesting playing field, pieces and rules.

As to the idea of using other shapes to denote cells in non-cubic fields
within a 2D medium, a simpler form might be to have points with colorized
radiating lines noting the various directions.  Like Chinese Chess, pieces
would move from point to point.

Although this might also be confusing as lines would criss-cross one
another without actually intersecting.  But this is where colorization
would come in handy.

But I don't think it is necessary to change the graphics for this
particular game as it is quite understandable in its current form.

Jared McComb wrote on 2004-01-08 UTCGood ★★★★
It seems to me that a true tetrahedral form of chess would have 'cells' which, in three dimensions, would take the form of rhombic dodecahedrons, which would allow the board to be pyramidial with 'hexagonal' tiled layers. (Rhombic dodecahedrons tesselate space quite nicely, you know, and naturally lend themselves to making tetrahedra with.) Does the current setup of this game allow for such an analogue? The board can be easily translated, complete with cell coloration and the same twelve directions, but can the rules be translated as easily? I'd love to see an attempt.

Charles Gilman wrote on 2003-06-21 UTCGood ★★★★
There is a sensible diagonal move on your board, although I can see why you
did you not use it as it is complex. On one level (literally rather than
the usual metaphorically!) the diagonal move is self-evident, along path
constant in colour and also in either letter or number. What a diagonal
move between levels means is determined by observing that the board can be
rotated into five other positions in the same frame (and reflected into
another six), which your noation recognises as they split evenly into your
levels I-VII, red-blue and green-yellow levels 1-7, and red-yellow and
blue-green levels a-g, revealing such diagonals as all the c4 squares.
Temperature goes out of the window (metaphorically rather than the usual
literally!), but is hardly needed once a diagonal capture has been found
for the Pawn.
	As well as this lot the board can be viewed with any corner as a
hexagonal cell at the top and the rest of it as six progressively larger
triangles of such cells down to 28 at the bottom. Each hex level has all
four colours and the diagonal move described in my first paragraph
requires a change of hex level.

LCC wrote on 2002-09-28 UTCExcellent ★★★★★
This has perhaps the most interesting geometry in a chess variant ever.
And if you take the time to actually make a board of the thing (paper,
tape and barbecue sticks spring to mind), the gameplay isn't even as hard
as in a geometrically coherent cubic chess.

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