Solving CycloHexane Isomerism: Find Total # Possible Isomers

[phoenixXL]

Question
Find out the total number of possible isomers with molecular formula C₆H₁₂ that contain a cyclobutane ring.

Attempted Solution

In Compound 3, Optical Isomerism is possible (geometrical isomerism is also possible but is neglected due to presence of optical isomerism) about both the branches, hence it will be counted as 4 isomers

In Compound 4, Geometrical Isomerism is possible about the two branches, therefore it will be counted as 2 isomers

Counting All : 1 + 1 + 4 + 2 = 8

Hence there are 8 isomers possible

Problem
The book where I found this question says that it consists only of 7 isomers.

Please help me out. Thanks for your time.

 

[Borek]

Check 3^rd.

 

[phoenixXL]

Yes, I was suspecting the argument with compound 3.

Please Verify
Compound 3 will have cis & trans forms. The cis form due to symmetry would not have optical isomers whereas the trans form would have optical isomers. As a result there would be three isomers (rather than 4).

 

[Borek]

Yes, 3 not 4.

 

[phoenixXL]

thank you for your time :)