This time we've figured out a word that can be used to refer generically to directions that are either vertical (up/down), lateral (left/right), or longitudinal (front/back). Our new word for this is edge-orthogonal.
Whenever most people need to refer to the full set of six fundamental directions within our 3-dimensional physical reality (or a subset of 4 of them on a 2-dimensional surface), they just spell it out in three words: "vertical or horizontal". But don't you think it's kind of wack that this takes three words, especially when we only need one to capture what is a strictly more advanced set of directions: those that are midway between these six basics? That one word, as you'll know, is the lovely "diagonal", whose Ancient Greek roots give it the meaning of "through the corners". So for example, in chess, we say that the bishop moves "diagonally", but the rook moves... "vertically or horizontally"?! Dave and I thought this was wack indeed — wack enough to warrant further investigation.
We found that some people, particularly in the context of board games like chess, simply use "orthogonal", that is, without the "edge-" prefix as we recommend. "Orthogonal" has a lot going for it; sharing the "-gonal" ending, it even sounds like a natural counterpart to "diagonal". But the reason why Dave and I don't find unqualified "orthogonal" satisfactory is because the primary mathematical definition of "orthogonal" is synonymous with "perpendicular", meaning at a right angle (90°); thus, if we were asked to, say, "move orthogonally", "draw an orthogonal line", or "indicate all of the orthogonal directions", it would beg the question, "Okay, but 'orthogonal' to what?". And so that's the question that our "edge-" prefix answers: whether you're looking at a chess board, a blank sheet of paper, or your living room, you should find some things that qualify as edges. Those are the things we want to be orthogonal to.
Now, we do admit a smidge of disappointment that "edge-orthogonal" is a hyphenated word; sure, it's technically one word, but it still feels like essentially-speaking we haven't quite made it down to one word from the three word "vertical and horizontal" (or "opposite of diagonal", I suppose). Though it's worth noting that in many contexts, you could get away with using "(edge-)orthogonal" the first time, i.e. parenthesizing the "edge-" prefix, then dropping it thereafter, using simply "orthogonal" once the reader knows what it is orthogonal to.
So while we'll be delighted if anyone else can find a suitable word that never needs a hyphen, after considering over fifty (!!) words ourselves over the past couple months, Dave and I think we've exhausted our powers here. Finding a word that is both versatile and clear while not having any deal-breaking issues turns out to be a pretty tall order! I'll spare you the details of our deliberations, but to give you a sense of what we talked about (and a head start if you do elect to pursue this problem further yourself!), here at least is the list I kept of all the words we rejected, in roughly the order they came up:
- nondiagonal
- orthogonal
- inradial
- diagrammal
- hedral
- diahedronal
- diaedronal
- diahedral
- diaedral
- apothemal
- sagittal
- axial
- t-wise
- additionsignwise
- axiswise
- gridwise
- cardinal
- crucial
- crucifixial
- roodic
- stauric
- daggeral
- obelic
- antidiagonal
- ectogonal
- sidewise
- edgewise
- dimensionwise
- rookwise
- tablewise
- latilongitudinal
- framewise
- horivertical
- updolerial
- monagonal
- lateral
- counterdiagonal
- nildiagonal
- interdiagonal
- gridical
- paraxial
- perpendical
- Cartesian
- cartesian
- quartesian
- paragrammal
- parakronal
- orthagonal
- orthegonal
- edge-parallel
- translateral
- dialateral