Will the dextrorotatory and laevorotatory enantiomers always have a set of stereocenters with opposite absolute configuration?

I was faced with a question where the skeletal structure of of D(+)-glucose was given and I was asked to give the right structure of L(-)glucose. I noticed that the correct answer was the one where all the stereocenters had opposite absolute configuration of those of D(+)glucose.


But my question is: Will the dextrorotatory and laevorotatory enantiomers always have a set of stereocenters with opposite absolute configuration?




Precisely, these are based on the configurations proposed by German chemist Emil Fischer, who established the structures of many sugars.



> 
> Emil Fischer elucidated these configurations for the aldohexoses in
>  1896. According to the Fischer convention, D sugars have the **same absolute configuration at the asymmetric center farthest removed from
>  their carbonyl group** as does D-glyceraldehyde. The L sugars, in
>  accordance with this convention, are mirror images of their D
>  counterparts,
> 
> 
> 


[![enter image description here](https://i.stack.imgur.com/bni8R.png)](https://i.stack.imgur.com/bni8R.png)


Similary,the Fischer projection for glucose is shown below.


[![enter image description here](https://i.stack.imgur.com/9muF4.png)](https://i.stack.imgur.com/9muF4.png)


It is very important not to confuse these **enantiomers** with **epimers** (two sugars that differ only in the configuration around one carbon atom e.g D-glucose and D-mannose, which differ only in
the stereochemistry at C-2)


[![enter image description here](https://i.stack.imgur.com/ctI6d.png)](https://i.stack.imgur.com/ctI6d.png)


References


* Voet and Voet Biochemistry
* Lehninnger Principles of Biochemistry
* Biochemistry (Campbell and Farrel)


 5