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I am currently studying Introduction to Solid State Physics, 8th edition, by Charles Kittel. In the section Fundamental Types of Lattices of chapter 1, the author says the following:

Crystal lattices can be carried or mapped into themselves by the lattice translations $\mathbf{T}$ and by various other symmetry operations. A typical symmetry operation is that of rotation about an axis that passes through a lattice point.

It's unclear to me what is meant by "rotation about an axis that passes through a lattice point". In doing research, I found this page, but I'm not completely sure that this is referring to the same phenomenon. I would greatly appreciate it if people would please take the time to clarify this. I would especially appreciate pictures depicting this, as well as the mathematics itself.

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    $\begingroup$ yes normal rotation about an axis, say, by 90 or 120 degrees, etc. but with the restriction that any symmetry operations causes the structure to be indistinguishable from that before the operation occurred. $\endgroup$
    – porphyrin
    Commented Jun 23, 2020 at 7:38
  • $\begingroup$ @porphyrin So exactly as is described here pd.chem.ucl.ac.uk/pdnn/symm1/rotate2.htm ? $\endgroup$
    – The Pointer
    Commented Jun 23, 2020 at 8:22
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    $\begingroup$ yes, same is true of all symmetry operations $\endgroup$
    – porphyrin
    Commented Jun 23, 2020 at 8:26
  • $\begingroup$ @porphyrin Ok, thanks for the clarification. $\endgroup$
    – The Pointer
    Commented Jun 23, 2020 at 8:29

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