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Man and Beast 01: Constitutional Characters. Systematic naming of symmetric and forward-only coprime radial pieces.[All Comments] [Add Comment or Rating]

💡📝Charles Gilman wrote on Sat, Jun 13, 2009 05:53 AM UTC:

While pieces may be bound to one of any number of mutually exclusive sets of cells, switching is always between two such sets - in the case of ranks, odd and even. The Bishop can move from odd to odd or even to even rank, as well as between the two, and so is not switching. Pieces that can move within a rank certainly do not switch ranks - although some like the Wazir switch other things. The pieces that always switch rank and file in 2d are the Ferz here, the Camel (and everything else -mel) in MAB 03, and the Bear in MAB 06 - pieces which always move an odd number of both. On a cubic board this is no longer the case as they can move within a rank.
	The matter of this page's compound pieces being unbound on a cubic board I hsve covered. The Primate, Pope, Besieger, and Usurper all have a Wazir move and so are clearly unbound. The Moderator and Heretic are unbound because they can move to an adjacent cell in two moves - by making a 1:1:1 move but retracting it in only two dimensions.
	All geometries' nonstandard diagonals have steps of length root-3 - the description asserting their common identity amounts to a root-2 and root-1 step at right angles.