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Fair enough, I should have said no 'simple' or 'elemental' piece. Tony Paletta's suggestion is certainly interesting. A slight difference from the FIDE Bishop is that the latter has only two varieties - light-square and dark-square - whereas the Paletta piece has six, with each hexagon covered by three of them. Combining forward/backward and sideways components can also be used for analogies the other way. Forward/backward Knight (the Heavenly Horse of Wa Shogi) plus sideways Dabbaba gives a square-board approximation to the hex Dabbaba of which I originally asked.