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Charles Gilman wrote on 2006-12-23 UTCGood ★★★★
I have been thinking further about pieces of this kind. It occurs to me that the Fox can be seen as a compound of two weaker pieces - a 'samewise' Fox that always makes two left or two right turns, and a 'contrariwise' Fox that always makes one of each. The first shares the Bishop's destinations but by a less direct route, the second those of the Lama (Dabbaba then Bishop) but with two turns instead of one. I take the 45° nature of the turn to apply equally in 3d, so that on both cubic and hex-prism boards the Fox still moves in only one plane in each move and so still has the same two components (but with more pairs of opposites than just left/right). The forward-only piece, the Foxcub, is always contrariwise. The Hyena, with 1:1:1 rather than 1:0:0 steps toppoing and tailing the Bishop section, would similarly have Samewise and Contrariwise components, but so would its forward-only version (Hyenacub?).

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