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Well, maybe there should be a way to refer to the comment to which one is
responding while one is writing his response; sorry I didn't address your
mention of the 'intragonal' move, which is a move from cell A to cell C,
separated by cell B and connected to each other only at one point, maybe
better described as 'going around the corner'of cell B, the cell between
them.

No piece goes around a corner of an intervening cell in Chess for Three.
Pieces have to move in straight lines, exiting their spaces along a path 
that begins at the theoretical dead center of the originating cell and
exiting either through the center of a wall of that cell, or through one
of its corners, then going whatever distance it's entitled in a straight
line.  To enable pieces to go around corners injects a move that I've
found confuses people because it is inconsistent with a fide analogy,
which would not permit skipping around a Cell B.  Perhaps there's a way
to use 'intragonal' moves in a triangular game, and perhaps some faerie
pieces move that way on square-cell boards, leapers, maybe (?), but it's
not needed or wanted in Chess for Three.