The Chess Variant Pages

[ Help | Earliest Comments | Latest Comments ]
[ List All Subjects of Discussion | Create New Subject of Discussion ]
[ List Earliest Comments Only For Pages | Games | Rated Pages | Rated Games | Subjects of Discussion ]

Single Comment

Octahedral Chess. 3d-board in octahedral form. (x9, Cells: 340) [All Comments] [Add Comment or Rating]
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.