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Piece aspects
In the absence of any better suggestions uit looks like I'll have to go ahead with my own ones. I have tentatively devised terming a rotating rectlinear piece Dual-inclusive if it includes 45° turns - with rules about how moves are affected, and Pivoted if it can turn no more than 45° either (or on a cubic board, any) way from its array orientation.
So if I read no better ideas by the time I go online on Sunday morning (about 48 hours from this posting) I'll post Starboard/Larboard Duals on Man and Beast 12, Dual-inclusive/Pivoted rotating pieces on Man and Beast 15, and Spearsman pieces on Man and Beast 16. In the meantime I'll add to Man and Beast 09 and 20 a few additional alternators which I have been mulling over.
Good choices, Charles, hoping to add to this specific suggestions before long of still other categories excluded for multi-path and separately for contingency pieces. One of the latter would be Ultima Coordinator you have not done. Contingency p-ts also include those moving on certain turns, or with certain check conditions, or like the General Staff in Novo Chess. Actually also, Prichard in Introduction to the first 'ECV' mentions there are tens of thousands of coordinate pieces. Pritchard uses the number 100,000 before the Internet came into being. Abbott's Coordinator would cross-categorize there too, and it's time to subdivide all three classes above, coordinate, contigency, and multi-path for widening nomenclature. I think not one example of those three piece-type subclasses appears in the year 2011 Guide either. They can be not itemized but systematized to some thousand p-ts by name-suffixes and -prefixes alone built onto the body of regular pieces, Wazir and Ferz, Bishop and Rook, then all the oblique ones.
Cannon/Canon of Jacks & Witches is dual-inclusive, http://www.chessvariants.org/large.dir/contest84/jacksandwitches84.html, as is Fourriere's Rook/Bishop of Polypiece43, http://www.chessvariants.org/43.dir/pocket-polypiece43.html. Gilman already links Centennial here, and its Rotating Spearman is not only Pivoted but found to be ''Sovereign.''
I have added Antoine Fourrière's inherently dual-inclusive pieces to Man and Beast 15. Obce I've read Symmetron in more detail I will include pieces that allow other pieces to rotate in Man and Beast 21, as they seem to fit with pieces that promote and demote other pieces.
The more I look at Symmetron the more of a one-off I see it is. Just explaining why some people use a term like Hippogonal would be quite a complication. Following an e-mail discussion with Christine Bagley-Jones I have other priorities for Man and Beast.
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Man And Beast 12 extends names for forward-only pieces to rectilinear pieces moving in any one orthogonal, any two neighbouring diagonal, or either two opposite orthogonal, directions in the face-to-face orientation - or any one diagonal, any two neighbouring orthogonal, or either two opposite diagonal, ones in the corner orientation - but none of the other six combinations. Yet two of this piece's rotations are of a piece moving along two opposite diagonals, capturing as one moving along a single diagonal, in the face-to-face orientation. Of course this is also true of the Delta of Omega Chess, which though mentioned in Man And Beast 15 could be considered inadequately described. This brings me to the next aspect.
Man And Beast 15 does not mention pieces that can be rotated only to face in forward directions, but this piece in each of its rotations has a well-defined forward move, the one in which it can capture. Even were it able to capture in both directions, it still cannot be rotated to move along a rank, but as it is, that brings me to the final aspect.
Man And Beast 16 does not cover pieces whose capturing moves are restricted to forward directions. For that matter nor does it cover pieces whose only capturing moves are in opposite directions to their only noncapturing ones, of which I do not recall any examples in variants.
I have some hazy ideas for terms for these piece aspects, but am not very satisified with them and would like to hear if anyone else has any. At first I considered terming a given forward-only or backward-only piece's compound with its Dexter the Dextered piece, the compound with its Sinister the Sinistered piece, the piece making only moves common to the piece and its Dexter the Desinistered piece, and the piece making only moves common to the piece and its Sinister the Dedextered piece, but that did not cover oblique pieces. What about a piece with only the two forward-right moves of the Knight, for example? My current thinking is to generalise the Larboard and Starboard to make a piece rotated 45° right and adjusted the original piece's Starboard Dual and rotated 45° left and adjusted its Larboard Dual - so the current Starboard and Larboard would be the Knave's Starboard and Larboard Duals respectively. I am looking at a Spearsman piece to mean one to which the noncapturing move in the opposite direction(s) has been added. For a piece that cannot rotate to or past the same-rank orthogonals I have as yet no ideas.