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I have two crystal structures, one in R3m and one in Cm symmetry. Both structures also differ in stoichiometric ratios, $ABC_4$ and $A_2B_2C_8$, respectively. Both structures look nigh on identical, with the exception of double the amount of atoms in one than the other.

How would I go about manually changing the symmetry of the Cm structure to R3m symmetry? I normally use VESTA as a visualization tool, and Avogadro as a tool for imposing symmetry.

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Your question is hard to answer because it lacks a lot of information. $Cm$ (IT #8) belongs to the monoclinic which does not say anything about the threefold symmetry axes present in $R3m$ (IT #160). But it is not unheard to transfer a monoclinic model into one that belongs to the trigonal / rhombohedral system.

Sadly, however, your question does not include a hint about the data and programs other than VESTA (for which I lack working knowledge) with you, nor your previous exposure to crystallography. Of course the best were to start all over with reducing the diffraction data to write a new .hkl file, now with the hypothesis of higher symmetry present, to solve and refine the model again. However, if you have a) a modern .cif file (those now including the hkl data and even better a good portion of the ShelX .res file), or b) one of the older .cif file plus the structure factors than you could give Platon's addsyminstruction a try. This routine was just written for the purpose of identifying missed symmetries. It will write you a new .hkl, for lattice constants already adjusted, and an .ins file (with Laue symmetry updated accordingly) to start over with ShelX or Olex2.

By today's standards, Platon neither truly is CLI, nor GUI (mainly a large FORTRAN 77 executable + X-window; executables available Linux, Mac and Windows), but well documented in publications by Spek himself including many worked test data. For addsym the page in question is here. Don't forget to check the model if it still is chemically sensible (bond lengths / angles, ADP ellipsoids, void volumes) and significantly better, e.g. by Hamilton's R-factor ratio test.

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