Hello, it's because your unit cell has a 120 degree angle and cos 120 = -0.5, 
sin 120 = 0.866. It reminds me of an essay I wrote in the lockdowns:

https://www.ucl.ac.uk/~rmhajc0/frorth.pdf

Best wishes, Jon Cooper.
[email protected]

Sent from Proton Mail Android

-------- Original Message --------
On 20/09/2025 14:45, Qixu Cai wrote:

> Dear Thierry,
>
> Thank you for your reply.
> After I provided the symmetric operator to PDB staff, they updated the matrix 
> as below:
> -0.500000 -0.866025 0.000000 89.06300
> -0.866025 0.500000 0.000000 51.42055
> 0.000000 0.000000 -1.000000 46.27767
> The matrix is totally different with the matrix I provided. How was the 
> symmetric operator (-X+2/3,-X+Y+1/3,-Z+1/3) transformed to the above matrix?
> The space group is H32 with cell constents of 178.126 178.126 138.833 90.00 
> 90.00 120.00.
>
> Thanks and best regards,
> Qixu Cai
> Email: [email protected]
>
> Fischmann, Thierry <[email protected]> 于2025年9月19日周五 23:37写道:
>
>> Hi,
>>
>> The matrix is correct for the operator you provide.
>>
>> Thierry
>>
>> From: CCP4 bulletin board <[email protected]> On Behalf Of Qixu Cai
>> Sent: Friday, September 19, 2025 11:30 AM
>> To: [email protected]
>> Subject: [ccp4bb] convert symmetric operator to matrix & coot1
>>
>> You don't often get email from 
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>>
>> Dear all,
>>
>> There is a dimer in the asymmetric unit of a structure, and applying the 
>> symmetric operator (-X+2/3,-X+Y+1/3,-Z+1/3) can generate a tetramer, which 
>> is a biological assembly. When I deposit the structure to PDB, I need to 
>> provide a matrix to generate the biological assembly. Is the following 
>> matrix correct for pdb format?
>>
>> -1 0 0 0.6667
>>
>> -1 1 0 0.3333
>>
>> 0 0 -1 0.3333
>>
>> Another question is that I can use "Calculate --> Modelling --> New molecule 
>> from symmetry op..." to generate new molecule in wincoot0.9.8. However, I 
>> cannot find similar function in new wincoot1.18. I also found that many 
>> useful functions in "Calculate --> Modelling" of coot0.9.8 are not available 
>> in coot1. Will they come back in the following versions of coot1?
>>
>> Thanks and best regards,
>>
>> Qixu Cai
>> Email: [email protected]
>>
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