Single Comment

People are still how there can be three orthogonal directions in a plane.
Because they are orthogonal to different things. Orthogonal is shorthand
for orthogonal to the cell boundar[y/ies] crossed. This is true of the
Rook move between square, hex, cubic, and hex-prism cells, and not of
Bishop moves.
Qualifications of diagonal clearly need not be used in a page referring
only to square boards or only to hex ones. Where they are needed standard
is shorthand for 'used in games that are or have been standard in their
part of the world' such as FIDE Chess, Chaturanga, Xiang Qi, and Shogi.
All these use either phyusical square cells or, as in Xiang Qi, something
functionally equivalent, and all use the same diagonal in terms of move
length and colourbinding (again even if squares are not physically
coloured differently). Nonstandard means 'different from that used in the
standard games' in terms of move length and colourbinding. Does anyone
expect a hex or 3d game to ever become a regional standard? Hybrid means
combining orthogonal moves at different angles to each other between
hex-prism cells. Regarding '3 at 90º or 2 at 60º' you must remember to
read it as following 'equal distances in...:' Only 2 hex orthogonal
moves can be mutually at 60º as a third at 60º to one would be at 120º to
the other.That the hex diagonal is not self-evidently a Bishop direction
is demonstrated by the oldest hex variant (Wellisch, 1912), in which there
is no Bishop and Knights move one square hex diagonal (Viceroys in my
terminology - the Queen is my Vicereine and the King a Xiang Qi General).
Noting that the faces of the tetrahedron in Tetrahedral Chess can be seen
as hex boards, it becomes apparent that the same kind of Knight is used
(invented independently, no doubt) there!