What dictionaries does triagonal appear in? It is not in Webster's 10th,
and it is not listed at dictionary.com. Although it does appear in the
OED, where it is described as an erroneous formation of trigonal, the only
definition given for it is triangular. The word is new to me, probably
because I don't play 3D games, and my objection to it arose from
Gilman's erroneous contrast between triagonal and diagonal, which
suggested that triagonal movement is not diagonal. As he said, hexagonal
boards 'have a triagonal but no diagonal.' Well, if that is what he
truly believes, then he is unaware of what you have just told me, that
triagonal is just a compression of tri-diagonal, for anything that is
tri-diagonal is still diagonal. My objection to the word stands because of
the confusion it can cause.

While I'm on the subject, I'll mention that this confusion has also been
engendered by our regular misuse of the word orthogonal, of which I have
also been guilty. The word orthogonal really means at right angles. The
directions that a Rook can move on a chessboard can be described as
orthogonal, because they are really at right angles to each other. But it
is just a relation between the two directions, meaning the same thing as
perpendicular, not an independent quality shared by each direction. The
most accurate word I can think of to describe the quality shared by the
directions Rooks can move on square and hexagonal boards is lateral.

Anyway, our misuse of the word orthogonal and our correct use of diagonal
has led to the mistaken notion that gonal is a proper root for use in any
neologism that describes an axis of movement in Chess variants. Gonal
comes from a Greek word for angle. Diagonal movement goes through angles.
So-called orthogonal movement goes through sides. To use common English,
we could speak of corner-wise movement and side-wise movement. For 3D
games, we could speak of corner-wise movement, edge-wise movement, and
face-wise (or side-wise) movement. When we use these plain English terms,
we can see that triagonal and diagonal are the same thing. They are both
corner-wise movement. In Raumschach, the Unicorn is the true 3D
counterpart of the Bishop, and it is the Bishop of Raumschach, not the
Bishop of hexagonal Chess, that does not move diagonally. It is called a
Bishop, because some of its movements through the cubic spaces of
Raumschach look like 2D diagonal moves from a flatland perspective, but
it, and not the Unicorn, is the truly novel piece in Raumschach.