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Octahedral Chess. 3d-board in octahedral form. (x9, Cells: 340) [All Comments] [Add Comment or Rating]
George Duke wrote on 2008-07-02 UTCGood ★★★★
From 1996 this is like my idea at Chessboard Math for 1x1 over 3x3 over 5x5 over 7x7, all centered totalling 84 squares. Ward's Octahedral carries on the other way, and its 10x10 become too many. Octahedral would be pretty good with 2x2 over 4x4 over 6x6 over 8x8, totalling 120. Opposed to write-ups, we accept the Pyramid board-space that flashed across the mind as hybrid of Thompson's Tetrahedral and this Octahedral probably noticed then. xxx

John Lawson wrote on 2003-06-15 UTC
Are you aware of the Yahoo group for 3d Chess?
There are links there to other 3-d chess sites as well.

Charles Gilman wrote on 2003-06-14 UTC
Further to my comments on the 2:1:1 leaper, the 2:2:1 one also has some interesting, and quite different, characteristics. Most obviously its leap length is an integer (2²+2²+1²=3²). The smallest integer leaper with two nonzero coordinates is the 4:3 Antelope (4²+3²=5²). Secondly a move 2 forward, 2 left, and 1 up followed by 2 forward, 2 down, and 1 right adds up to 4 forward, 1 left, and 1 down - and the leap of the 4:1:1 leaper is root 18. This means that the 2:2:1 has moves at right angles to each other, usual among leapers with two nonzero coordinates but rare among those with three. Finally it has no colourbinding. Indeed if you divide the square of any leap length by four remainders indicate: 1 no colourbinding, 2 diagonal colourbinding, and 3 triagonal colourbinding. Those dividing exactly are non-coprime and therefore even more bound.

Charles Gilman wrote on 2003-05-17 UTCGood ★★★★
It is great to see constructive comments taken on board so quickly. I recently discovered an extraordinary feature common to the leaper you call a Camel (2:1:1) and the one more commonly called a Camel (3:1:0). Both can lose the move in 3d, that is, return to a square in an odd number of moves (5 minimum). It is notable because the 3:1:0 leape rcannot lose the move on a 2d board! In general root-odd leapers cannot even lose the move in 3d, and root-even ones can lose it in 3d if their leap does not pass through the centre of a cell of the other Bishop colour, but not in 2d. Thus the Ferz and Alfil can lose the move in 3d but the Dabbaba cannot.

Charles Gilman wrote on 2003-04-19 UTC
1	You rightly point out that it takes 4 of your Elephants (called Unicorns
in e.g. Raumschach) to cover the board, yet you have only 2 aside, and
they cannot capture each other. Is this an oversight or a deliberate
attempt to emulate the original Chaturanga Elephants which cannot capture
each other?
2	Camel usually means a 3:1:0 leaper, although that piece might also be
useful. I have seen the 2:1:1 called the Sexton (a pun on the leap length
of root 6, although the word actually derives from sacristan).
3	Finally, combinations of 2 as well as 3 elemental pieces are valid in 3d
Chess. Indeed you could even have a hybrid of long-range radial and
short-range oblique. I could list some stanadrd and suggested names if you
are interested.

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