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# Single Comment

Octahedral Chess. 3d-board in octahedral form. (9x(), Cells: 340)
Charles Gilman wrote on Sat, Jun 14, 2003 07:27 AM 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.

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