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If I take a shape and its mirror image, what is the word for the property in which the two differ? For example, they differ in position after a translation, or orientation after a rotation.

If the original shape had its vertices labeled clockwise, then this word would pick out whether or not the vertices remained clockwise or not (and would still apply for non-chiral shapes like squares where the mirror image would otherwise look the same).

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    For (samples each containing a different one of) two chiral molecules constituting a mirror-image pair (optical isomers), the word 'enantiomerity' has very occasionally been used in the literature for this. '... characteristic mass spectra and their enantiomerity determined ...' {Helmholtz ...} – Edwin Ashworth May 8 '18 at 18:47
  • Translations and rotations can occur in the real world as well as on paper, but reflections are confined to the notional realm. Position and orientation do not need to presuppose a transformation has taken place. Perhaps one should not expect a corresponding word relating to 'initial shape and oppositely congruent shape'. Maybe 'sense' has been used, but the word already has a lot of senses. – Edwin Ashworth May 8 '18 at 22:10
  • @dbmag9 I'm afraid your question moves the goalposts. An "achiral" square changes nothing when it's reflected. But if you do something such as label the vertices, then you've gone and introduced chirality to the system. You can't have it both ways. – Spencer May 9 '18 at 9:47
  • @EdwinAshworth This reminds me of the time my high-school German teacher asked me "why does a mirror reflect left-to-right but not up and down?" without realizing he'd introduced semantic confusion into simple orientation terms by the framing of the question. – Spencer May 9 '18 at 9:58
  • @Spencer OK, sure, but per the definition below, a chiral shape (for example a handprint) remains chiral after (any) reflection. So since both the original and its image are chiral, it is not the property changed by reflection. An achiral square remains achiral after reflection. – dbmag9 May 9 '18 at 10:39
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Chirality

The characteristic of a structure (usually a molecule) that makes it impossible to superimpose it on its mirror image. Also called handedness.

The American Heritage® Science Dictionary. Copyright © 2002. Published by Houghton Mifflin. All rights reserved.

Informally, you can get away with just using "handedness", because "chirality" is just Lord Kelvin's Hellenized version of the English word. This comes from the fact that most people's left hands are rough mirror images of the corresponding right hands.

When you're introduced to vector spaces, you'll learn about the "right-hand rule" which determines the direction of a cross product.

You might enjoy Martin Gardner's book The New Ambidextrous Universe, which explores many aspects of symmetry and charality/handedness.

You've asked what happens to an "achiral" object like a square, but you've inadvertently asked about two different systems. An "unlabeled" square is achiral and changes nothing when it's reflected, because we don't care which vertex is which. But if you go and do something such as label the vertices, then you've introduced chirality to the system.

Essentially, you've taken an undirected graph and turned it into a directed one. Draw a square on a piece of paper, then label its vertices clockwise. Then, reflect the graph in a mirror (or look through the other side of the paper). The labels you see will be counterclockwise.

  • I don't believe this captures what I'm looking for, for the reason that Edwin Ashworth sets out. Analogous sentences would be "the square has changed its orientation after a rotation by 90 degrees, although because a square has rotational symmetry the image seems identical" and "the square has changed its X after a reflection in x = 0, although because a square is non-chiral the image seems identical". I am looking for the analogue to "orientation". – dbmag9 May 9 '18 at 9:01
  • @Spencer I'm not especially bothered, but do try to be careful about making assumptions like in "when you're introduced to vector spaces" – I have a master's degree in mathematics and philosophy from Oxford. – dbmag9 May 9 '18 at 9:04
  • If you'd given the relevant defintion from your reference, all this could have been avoided. The Collins entry: << chirality noun 1. the configuration or handedness (left or right) of an asymmetric, optically active chemical compound Also called dissymmetry >> So this is a complementary definition to 'the characteristic of a structure (usually a molecule) that makes it impossible to superimpose it on its mirror image' 'Also called handedness' does not entail the relevant definition. – Edwin Ashworth May 9 '18 at 15:11

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