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64 triangles. Missing description (8x8, Cells: 64) [All Comments] [Add Comment or Rating]
George Duke wrote on Tue, Oct 19, 2010 03:23 PM UTC:
(I) Infinite the tesselations there are whatever the chosen polygon, Frolov said the last comment. Yet equilateral triangle is the right root expression.  Just as OrthoChess is/has been square of squares, so it could be better equilateral of equilaterals,  [ChessboardMath12 has 18 comments, so this one       
    .         is put here of variety.] Drawn to left is 3x3x3 or 3^2 
   . .        in adaptable notation. The sizes correspond squares to
  . . .       triangles: 9,16,25,36,49,64,81,100.... Square is 10x10 
 . . . .      and triangle is 10x10x10 in 2-d.  As Frolov intimates,
__*Classical Tetraktys at left above*__
which is more fundamental, square or triangle?  Which is the portal out of dark forbidding one-dim to two-dim?  Must not even superior Mayans have triangulated to achieve the 26000 earthly precession cycle accurately? How many fundamental pieces are there in more perfect triangles, regularly equiangular pi/3? Three (which suggests fundamental pieces equal number of sides in any uniform tesselation, for follow-up, 3 -> 3; 4->4...)
(II) Restrictive term 'triangulate' means something different in Chess play itself of course. All OrthoChess so far knows is that King or Queen triangulate, return in three, but variantists discover others.  Now as sounding irony, natural basic triangular omni-Pawn, moving/capturing through side, on 8^3 or 9^3 or any of them, is unable to ''triangulate.'' The Pawn (who travels like Frolov's Rook here one-stepping) can neither quadrangulate nor quintangulate. Once that (Centennial Chess Steward-like) Pawn steps from his triangle, he can only circumnavigate in six.  Far more likely if he returns, it is a backstep not an hexangulation.

💡📝Daniil Frolov wrote on Sun, Oct 17, 2010 01:57 PM UTC:
Actually, there is infinitive number of possible triangle tesselation: any polygon can be divided into triangles (number of triangles is same as number of i's sides). In all triangle variants i know this polygon is hexagon, in tesselation i suggested, it's rectangle. And large triangles, composed of triangular cells can be arranged in same ways as cells.
But there are two most interesting tessellations, i see: the own that i described before and 3 triangles arranged in one large triangle, 3 such large triangles are arranged into larger triangle, and so on (it should have 27 or 81 cells).

💡📝Daniil Frolov wrote on Wed, Oct 6, 2010 11:12 AM UTC:
Another close eqivalent of standart chess: bishop is same, rook moves as spire ( ), knight moves as compound of my knight and ninja. Other pieces are based on them.

💡📝Daniil Frolov wrote on Tue, Oct 5, 2010 07:02 AM UTC:
Another interesting triangle variant would be board, consisting of several suares, and each square consist of 4 triangles, and each triangle is playing space. I have not thought about pieces for such board yet, but idea is interesting.

George Duke wrote on Tue, Oct 5, 2010 01:36 AM UTC:Good ★★★★
This is good and the best way to use triangles to advantage in a board along with corresponding 9x9x9.  Here is what I did with the same 8x8x8: The pieces and type movements need to be compared in the two efforts as time allows. The progress also suggests in roundabout way that we should attack 64 squares as ridiculously obsolete and narrow of past centuries. Frankly standard 64 squares is considered a waste of time to vast majority of its former core audience of elite -- very much including the recently educated, one and all seeking ultimate mental challenge. That percentagewise decline holds from Brazil to Russia to Australia notwithstanding manufactured Internet numbers that can be generated. 
Such an argument is already spread around the CVPage and would need organization, unable to justify in few sentences of a comment or two.  As the present instance, Triangles, once settling on the correct triangle boards, 2 or 3 at most, then the lesser products some things like 6x6x6 or 10x10x10, or mix of squares and triangles, or right angle triangles -- these abortions become as uninteresting as they are inferior. Do them in the privacy of your home if you have to. Or enter them into popular culture at risk of ridicule.
So now, following through on Triangles as themed example,
every design of different creative win condition or piece mix will naturally 
follow suit, staying with or reluctantly varying from triangular 8^3 and 9^3.  There are still millions of 8x8x8 (of triangles) to deal with. 
NextChess itself, soon to include a hexagonal, and 
already having a 3-player, for two irregular examples still legitimate next chesses, as defined, is sustained by this breaking away from pure artwork as such towards logical irrefutable scientific directionality.

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