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H. G. Muller wrote on Wed, Nov 11, 2020 01:56 PM UTC in reply to Jean-Louis Cazaux from 12:38 PM:

Not wrong, because 'counter-part' is a more loosely defined term than 'conjugate'. The latter I have seen only used in the meaning I gave previously. Basically, the conjugate piece is what you get when you grow a new diamond-shaped square in every square corner of the board. Which means it is not a symmetric relation: The Ferz is the conjugate of the Wazir, but the conjugate of the Ferz is the Dababba. The Camel is the conjugate of the Knight. Conjugates by definition are color bound. The conjugate of the W-then-B would be the F-then-DD (as the conjugate of B is the Dababbarider)

In XBetza notation I introduced the term 'rotation' of an atom, which is a symmetric relation: F is a 45-degree rotated W, and W is a 45-degree rotated F. Similarly A <-> D and R <-> B on rotation. So I guess one could say the Gryphon is the rotated 'Rhinoceros', and vice versa. The large Shogi variants often employ this 'playful symmetry', where pairs of pieces in mirror-image positions of the setup interchange orthogonal for diagonal moves of the same range, and vice versa.

I used this W-then-B in my variant Team-Mate Chess, because it is a quite strong piece without mating potential. (And the design goal of Team-Mate Chess was that it would always require at least a pair of pieces to beat a bare King.)


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