George Duke wrote on Tue, Mar 9, 2010 05:06 PM UTC:
Falcon first-steps like the Knight, but Falcon is always three steps and
blockable. In equilateral triangles, Knight leaps more in a straight line,
differently from squares. Knight leaps either through a vertex or through a side for
6 destination cells, not squares' eight. Where Knight goes through a side,
Falcon has three potential arrival cells, just described,
http://www.chessvariants.org/index/displaycomment.php?commentid=25201.
Where Knight would go through a vertex, corresponding Falcon manoeuvre is called back-Falcon, who is three-way to the three logical spaces. Falcon, front or back, can
never use Bishop's cells en route. The four basic moves, R-N-B-F quickly
become second nature in any regular geometry, square, triangle, hexagon.
http://www.chessvariants.org/index/msdisplay.php?itemid=MSfalconhexagona
Abdul-Rahman Sibahi already worked it out here in less manageable hexagons. With all the foregoing movement formulae, there is complete mutual exclusivity of arrival squares, with the understanding that Queen's assuming Bishop and Rook modes offsets appropriately their individual infinities.