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I recognise the piece called a 'Rook' here. The idea of a piece moving straight forward/backward/sideways on a hex board was put to me when I claimed that there was 'no piece bound to half a hex board' although the Dabbaba is bound to a quarter of it. I eventually documented it in my piece article Man and Beast 12: Alternative Fronts - you can find it by searching on that page for Moorhen. It is defined by the straightness of the directions (and of up and down on a hex-prism 3d board) regardless of whether they are orthogonal or hex diagonal and whether the orientation is Wellisch, Glinsky, or hex-ranked.
The labels for the directions are somewhat confusing as 'oblique' usually indicates a direction such as that of the FIDE Knight, going through intervening cells off-centredly. A more accurate description for the directions of each colour are forward/backward hex-diagonal, sideways orthogonal, forward/backward orthogonal, and sideways hex-diagonal. The linepieces in these directions I term Unicoranker, Rookfiler, Rookranker, and Unicofiler. These definitions also work on a Glinsky board, but on that it is the first two that have four directions and the second two only two.
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