In the following figure, is it automatically correct and clear to say that

X is axially symmetric to Y with respect to Z


Is there any better way to express this fact?

enter preformatted text here

  • 3
    This is one of those "dangerously close to proofreading questions." :^) As for "Is there any better way to express it?" that depends on your audience. In a bar talking with friends, I might say, "X is the mirror image of Y." When giving a technical presentation at a conference, though, your wording might be better – not because the words are "fancier," but because they are more mathmatically precise. In short, axially symmetric is understandable, but rather atypical in everyday conversation.
    – J.R.
    Nov 15, 2014 at 23:45
  • @J.R. Thanks, I understand. I haven't done much geometric in English so I wasn't very confident :) I guess the border between word usage and proofreading is narrow! Nov 15, 2014 at 23:49
  • Z is a line of symmetry for X and Y.
    – Jim
    Nov 16, 2014 at 7:36
  • 1
    I think saying the shape has reflection symmetry, or the shape is bilaterally symmetric is a better choice. Saying axially symmetric, though applicable, usually implies three-dimensional objects. Nov 16, 2014 at 9:10
  • @Franck: As for the narrow line between word usage and proofreading, you can always make that a wider boundary by doing and including more research. Questions like "Does this sound okay?" sound like a request for proofreading. Questions with supporting research (such as, "I know this phrase is commonly used, because I found more than 300,000 instances on Google; however, I'm wondering if those words sound too scientific, or if they are readily understandable") sound like a question from someone who knows what they want, has done their homework, and still needs some guidance or help.
    – J.R.
    Nov 17, 2014 at 10:23

1 Answer 1


In formal speech or writing, you could say, "The shape is axially symmetric." The symmetry would be sufficient to identify the axis of symmetry (Z). If you were making a formal geometric proof, you might need to provide additional details, like "Z is the axis of symmetry."

As J.R. points out, you could say "X is the mirror image of Y." This is appropriate in both formal and informal contexts. As J.R. points out, it is appropriate in ordinary conversation. It is also appropriate in Physics texts and lectures. Unless you have explicitly defined the concept of a "mirror image", it probably would not be appropriate in a geometric proof.

As Demkemg points out, "axial symmetry" and "bilateral symmetry" are equivalent for 2-D objects. For 3-D objects, "bilateral symmetry" is the same as "mirror" symmetry; both are with respect to a symmetry plane. Also for 3-D objects, "axial symmetry" is the same as "radial symmetry", especially when viewed from a point along the (linear) "axis of symmetry".

2-D is short for "two dimensional" or "planar". 3-D is short for "three dimensional".

"Axial symmetry", "bilateral symmetry", "radial symmetry", "axis of symmetry", and "planar" are all formal. They are appropriate in Physics and Geometry lectures and texts.

"2-D" and "3-D" are informal, and appropriate in ordinary conversation. "Two dimensional" and "three dimensional" are more formal; they sound out of place in many informal conversations.

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