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Is there a word for the union of orthogonal and diagonal? If used in a sentence:

The queen in chess can move ______.

And used in another sentence:

There are infinitely many directions. My pet robot can only move vertically, horizontally, or diagonally at 45 degree angles (a total of eight uniformly distributed directions). My pet robot can move ______.

The rules for chess describe the queen as able to move vertically, horizontally or diagonally. Just as vertically and horizontally can be condensed into a single word, orthogonally, I was hoping to condense all three to a single word.

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    You can say the queen can move in all cardinal and ordinal, or in any of the eight principle, directions.
    – Dan Bron
    Commented Feb 3, 2015 at 23:12
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    The queen can move any direction the king can move, only farther.
    – Hot Licks
    Commented Feb 3, 2015 at 23:16
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    Octopussianly, while not in any dictionary, is evocative.
    – user63230
    Commented Feb 3, 2015 at 23:31
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    @Rainbolt: I need clarification on what you are asking for. Your example of the pet robot confuses the issue. Are you asking for this word in a chess-like or chess-only context (grid-based 8 directions max) or for ALL "orthogonal and diagonal" movement including non-45° angles ("infinite directions")? If the former than the mouthful of octilinearly as suggested below by Jimi Oke fits well indeed. If the latter then I humbly submit my radially usage below.
    – O.M.Y.
    Commented Feb 4, 2015 at 12:39
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    On an aside, the use of the word "vertically" is somewhat in error as that would imply Z-axis motion akin to levitation ("my pet robot has antigrav boosters"). Of course if you are referring to 3D chess or Star Trek chess then vertically is a possible movement direction for all of the pieces.
    – O.M.Y.
    Commented Feb 4, 2015 at 12:47

7 Answers 7

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I have been doing some academic research in this area. The current coinage, which I think perfectly applies to the movement of the queen in chess, is octilinear. This term has been used to describe metro-map layouts that have followed Harry Beck's paradigm. The vertices of a unit-spaced octilinear grid describe the queen's range of motion (in multiples of 45 degrees; four axes and eight possible directions). So, to complete your sentence:

The queen in chess can move octilinearly.

Octilinear grid

The most recent journal paper in the schematic mapping field is: Octilinear Force-Directed Layout with Mental Map Preservation for Schematic Diagrams. And a search on Google scholar will show that octilinear is now a widely-accepted term, that hopefully will move into mainstream vocabulary!

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    But that applies in a 2-dimensional world. What would it be called in 3D, or even better - nD?
    – Konrad Viltersten
    Commented Feb 4, 2015 at 15:15
  • @KonradViltersten In all honesty, that's a technical question about mathematics or engineering, and not about English, since I doubt such term is widely used in any language. Maybe Mathematics would be a better place for it?
    – yo'
    Commented Feb 5, 2015 at 9:08
  • @yo'Well, the reply I was commenting on opened for the scientific lingo, so I felt it was called for. But generally speaking, I agree with you. It's so seldom used that there's little risk there's an non-mathematical term for it anyway.
    – Konrad Viltersten
    Commented Feb 5, 2015 at 11:18
  • @KonradViltersten Great question! I have no idea what the appropriate term might be in n dimensions...
    – Jimi Oke
    Commented Feb 5, 2015 at 17:42
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Well, this is a coinage opportunity, although perhaps, given that octolinear has sneaked in first, a fading one.

As a straightforward composition in the German tradition of piling together existing words, we could say that a queen moves orthodiagonally. As Scott Centoni observed, this might support extension into higher dimensions also.

As an imagery-based coinage to support the idea of the queen's move to other applications, you could say that the queen in chess moves majestically. So does the king, but more slowly.

And then Jimi Oke's referenced paper could talk about about Majestic Force-Directed Layout...

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    I'm having fun conjuring up images of a pet robot moving majestically.
    – 200_success
    Commented Feb 4, 2015 at 9:42
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    @Joffan: While I love your suggestion for its creativity I do not think it will fly. :( On the other hand I was inspired to my own "coinage opportunity" by your post, albeit a more pedestrian one involving re-purposing an adjective to a new usage as an adverb. See above.
    – O.M.Y.
    Commented Feb 4, 2015 at 12:17
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    Majestically is cute, but I like orthodiagonally better than octalinearly because it does generalize better for arbitrary dimensions >=2.
    – Scott Centoni
    Commented Feb 5, 2015 at 1:07
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    Definitely not majestically but I do like orthodiagonally!
    – Jimi Oke
    Commented Feb 5, 2015 at 17:45
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    @JimiOke - yes... I rearranged my answer to promote the constructive over the allegorical coinage :-)
    – Joffan
    Commented Feb 5, 2015 at 17:53
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octagonal neighbors/directions/moves

In the 15th century, mathematicians decided to combine Greek words with Latin flavoring to form new terms, and they came up with:

  • from dia- "across/through" + gōnia "angle/corner" => diagonal
  • from ortho- "straight" + gōnia => orthogonal

and similarly

  • from okta- combining form of okto "eight" + gōnia => octagonal

I wonder why we refused to assign relational/spacial meaning to word octagonal and only use it for describing shape of things. The way this word was formed is identical to the other siblings, and we are happy with diagonal and orthogonal directions. I stand for octagonal directions. Poor guy deserved it :)

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For lack of a better (i.e. existing) word, I'd probably use octantally

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  • I gotta give you credit for dredging that one up.
    – Hot Licks
    Commented Feb 3, 2015 at 23:15
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    "Octant" usually means the three-dimensional analogue of a quadrant. I'd be confused by such usage.
    – 200_success
    Commented Feb 4, 2015 at 9:40
  • Interesting word, I could have used that many years ago when I was tinkering with programming Star Trek games in BASIC. :)
    – O.M.Y.
    Commented Feb 4, 2015 at 12:20
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How about "radially" ?

Technically this word is an adjective but I see no reason why it could not be applied as an adverb in this context per the first part of definition #3 below.

adjective

  1. arranged like radii or rays.
  2. having spokes, bars, lines, etc., arranged like radii, as a machine.
  3. made in the direction of a radius; going from the center outward or from the circumference inward along a radius: a radial cut.
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    "radially" is a perfectly good adverb already , and not a bad choice, although its association with circles does mean that I think of the possible directions as unlimited rather than restricted to 8. But don't let my mathematical background slow you down. :-)
    – Joffan
    Commented Feb 4, 2015 at 14:10
  • Mathematically speaking, it's too relaxed. Consider the horie's move. Effectively, it moves radially too but it's eight direction are not equidistantly spread (or, even more exact, they are offset from the queen's movement angles by an angle).
    – Konrad Viltersten
    Commented Feb 4, 2015 at 15:19
  • Strictly speaking, every piece moves radially, only the angle of said radius is restricted.
    – J A Terroba
    Commented Feb 4, 2015 at 19:56
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I would prefer the term "Holonomic" from the robotics realm.

If you have a robot base that can move in any direction from any orientation, this type of drive is often called holonomic.

http://en.wikipedia.org/wiki/Holonomic_(robotics)

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  • Total degrees of freedom in the robotics realm: infinite. Degrees of freedom of the robot in the question: eight. Therefore, the robot in my question is not holonomic.
    – Rainbolt
    Commented Feb 4, 2015 at 21:56
  • @Rainbolt 45-degrees-increment-based-holonomic, then? There's probably some weird planet where this term is commonly used, hehe.
    – Konrad Viltersten
    Commented Feb 5, 2015 at 22:49
  • @KonradViltersten How about holonomic-but-not-really?
    – Rainbolt
    Commented Feb 5, 2015 at 22:54
  • @Rainbolt Naa, no way. You're loosing the oh-so-crucial information about equidistant partitioning into eight available directions. (Seriously, though, I believe your term is much less eye-brows-raisable, hehe.)
    – Konrad Viltersten
    Commented Feb 6, 2015 at 10:52
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A short phrase might be in a straight line.

If you want a single word, how about queen-style?

While there are infinitely many directions, your pet robot can only move queen-style.

Of course, this doesn't work when describing Chess rules.

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  • I like queen-style. I don't like in a straight line. It doesn't limit direction to only eight possibilities.
    – Rainbolt
    Commented Feb 4, 2015 at 22:31

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