When calculating a dihedral angle for a chemical bond, how is the direction defined? What are the most common convention?

I understand the geometry and calculation of a dihedral angle, discussed in [this question](https://math.stackexchange.com/q/47059/221321). It is not clear how the direction is defined for a chemical bond. On the [wiki page for dihedral angles](https://en.wikipedia.org/wiki/Dihedral_angle), it states that, "the dihedral angle $\phi$ is the counterclockwise angle..." between the planes $P\_{123}$ and $P\_{234}$ (where $P\_{123}$ is defined as the plane containing atoms 1, 2, and 3 in the diagram below, and likewise for $P\_{234}$).


$\hspace{45 mm}$![bonds](https://i.stack.imgur.com/DiwKp.png)


This counterclockwise definition means that the direction of the dihedral angle is defined using the left-hand rule about the line connecting atom 2 to atom 3. The left-hand rule is unusual in mathematics and geometry. Alternatively, this example may be defining the directionality of $\phi$ simply so the result is a positive angle less than $180^\circ$. 


I have not been able to find any chemistry standards on this. Is there a common convention?




The [IUPAC Gold Book](http://goldbook.iupac.org/T06406.html) states that, 



> 
> In a [Newman projection](http://goldbook.iupac.org/N04134.html) the torsion angle is the angle (having an absolute value between 0° and 180°) between bonds to two specified ([fiducial](http://goldbook.iupac.org/F02356.html)) groups, one from the atom nearer (proximal) to the observer and the other from the further (distal) atom. The torsion angle between groups A and D is then considered to be positive if the bond A-B is rotated in a clockwise direction through less than 180° in order that it may eclipse the bond C-D: a negative torsion angle requires rotation in the opposite sense.
> 
> 
> 


This implies a range of -180 to 180, which is by far the most typical range used, but I certainly have seen reports ranging from 0..360, e.g., 225 degree dihedrals. 


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