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Thank you, Charles, for providing this overview and glossary. It gives me a point of reference to look at your work with maybe some understanding. I've got a couple of questions, one general, and one specific. 

The general question concerns how to look up pieces. Several of us here have designed pieces, and might like to know how and where they fit into your scheme. I recognize some of Mats' pieces, I see George's Falcon family is there, and I even see Gavin Smith's planar pieces from Prince there. I think Larry Smith [no relation] played with planar pieces against Gavin, but Larry also did a rather thorough and extensive classification of Jetan pieces. It was Larry's monograph that made me realize how lucky I was not to have re-invented ERB's [and Larry's] pieces with some of my designs. So could I look up ERB's pieces, or my own pieces like the shaman or the flexible knight, in some systematic way? 

The second question is about planar pieces. Gavin and Larry seemed to agree [and I hope one or both will comment if I make a mistake] that planar pieces were 2D pieces that had to take every possible shortest path from their starting location to their ending location when they moved, and any single piece on a single one of those multiple locations making up all the shortest pathways from start to finish would block the move. I believe you also seem to accept their definition. I'd like to argue again [as I did with Larry, then], that this is far too restrictive a definition. 

Let's take a simple example of a planar rook and its target, an enemy planar bishop, 5 squares away diagonally, on the same 2D level/board section/whatever. Anyway, the planar rook can take the bishop if all 23 of the squares between the B and the R that occupy the 5x5 2D square [determined by using the positions of the B&R as opposite corners of the square] are empty, according to the rules. This is the weakest form of planar piece. [It's equivalent to damming a river by throwing a rock in it. To marginally mitigate this, there are 2 2D planes, and only 1 needs to be clear.] 

The strongest form of planar piece would be able to take if only one of all the shortest paths was open. An average planar piece might see the cut-off at half the paths available. A weakest cubic rook, B&R at opposite corners of a 5x5x5 cube, would require 123 empty cubes to capture the bishop. The bishop, being colorbound, would only need roughly half as many locations clear to effect a capture in general [and in the example given, only 3 empty cubes], thus more than overcoming its colorboundness to be worth more than the rook, no?