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Martin Turner

Stereochemical relationship between the given compounds

Dawn Le Strat  Follow

The given compound, 1,2-dimethylcyclobutane has two chiral centers, and hence, has maximum of $2^2 = 4$ stereoisomers. However, as shown in the scheme below, the cis-isomer has a plane of symmetry, and as a consequence, it is a meso-isomer:

1,2-Dimethylcyclobutanes

However, trans-isomer can exists in two forms: (1R,2R)-1,2-dimethylcyclobutane and (1S,2S)-1,2-dimethylcyclobutane (see Scheme $\bf{A}$).

The two isomers given in the question are both trans-isomers. Thus, they woul be either identical or enanthiomers as shown in the Scheme $\bf{A}$ (cannot be diastereomers). Although, the OP's visualization is correct and can use to identify simple molecule like this, it is hard to visualize if presented complex molecule. The best way to identify stereoisomers are assign their appropriate (R/S)-configurations as I have done for OP's structures (see Scheme $\bf{B}$).

Accordingly, both structures are (1R,2R)-1,2-dimethylcyclobutane. Thus, the compounds are identical.

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