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enter image description hereWhat is a "unique" mirror line of symmetry? For example why does an equilateral triangle have three mirror lines but only one "unique"mirror line of symmetry?

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  • $\begingroup$ What is the difference between a "mirror line" and a "mirror line of symmetry"? It sounds to me like they should both mean the same thing, and an equilateral triangle indeed has three of them, not one. $\endgroup$ – mdp May 1 '14 at 15:09
  • $\begingroup$ I think you're just confused, this concept doesn't make sense to me. Make sure your sources are correct or post them here. $\endgroup$ – Patrick Da Silva May 1 '14 at 15:17
  • $\begingroup$ I came across this in a Coursera course on symmetry and am myself confused. The Prof shows a four leaf clover and says it has 4 mirror lines of which 2 are unique. $\endgroup$ – pirsquare May 1 '14 at 15:22
  • $\begingroup$ Is it possible to upload an jpeg here? $\endgroup$ – pirsquare May 1 '14 at 15:23
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    $\begingroup$ Probably they mean that the three mirror lines can be mapped to each other by symmetries of the triangle, so that they are "all the same" = "unique". (Yes, strange use of the word "unique"...) For the clover, there are two kinds of mirror lines, diagonal and horizontal/vertical, where each kind cannot be mapped to the other by a symmetry of the clover. $\endgroup$ – Hans Lundmark May 1 '14 at 17:01
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Some Googling turned up this excerpt from what appears to be the transcript of a Coursera lecture on this topic:

If we take a hexagon then evidently, there are mirror lines but we can draw them in two different ways. We can either draw mirror lines which are passing through the vertex of the hexagon and you would have three of those. Or you can draw those mirror lines passing through the face of the hexagon and there are three of those [...] so that's why we would say they are mirror lines of only two types.

So insofar as this topic is concerned - since it clearly is not emphasizing a rigorous presentation of definitions - it seems that you should consider a "unique" mirror line to refer to the equivalence classes of mirror lines, up to congruence of the mirrored halves.

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Because the shape when cut using mirror lines are different. For example, the shape when you use vertical and horizontal mirror lines, the shape of clover is the same (2 petals of clover). When you use the diagonal mirror lines, the shape of clover is again the same but different from the horizontal and vertical mirror lines (1 petal +2*0.5 petal). Hope this helps

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